Applied  modelization to electricity markets, as a financially unstable complex system
Autor: Manco Lopez, Oscar Oswaldo
Asesor: Camacho Moreno, German (Thesis advisor)
Fecha: 2016-11-16
Programa: Bogotá - Medicina - Especialidad en Anestesiología y Reanimación
Facultad: Facultad de Medicina

Resumen: The challenges faced by different sectors of the economy, respond to the evolution and specialization of consumers and producers, where the needs are becoming more complex. In this sense, during the last 5 years the electricity markets have undergone an evolutionary pro- cess that aims to meet the needs of all stakeholders in the midst of sustainability scenarios. Thus, the agents involved in the electricity market, present a num- ber of exhibitions of operational nature, legal, ethical, financial, among others, which require a specialization allowing the entry of new tech- nologies. This research project focuses on the study of financial risk, which despite being so specific, consider many elements with the aim of ensuring the functioning of the market and its participants. In previous studies, some models have concentrated on the in- vestigation of blackouts phenomena, the stability of the network, the dynamic power system, and Smart grids, among others. Mean- while other investigations have addressed the problem of forecasting different variables like the spot price and corporate strategy, with the aim of increasing the profitability of the participants. Now, this project presents the proposal of a complex financial model, which results in calculating a market equilibrium considering initial condi- tions and risk constraints. Using game theory it demonstrates equi- librium instability and that through complexity it is possible to find an optimal scenario in terms of profitability for the system and the agents. In chapter 1 it carried out a review of previous studies in order to justify the investigation, then Chapter 2 includes a description of the Colombian electricity market, with different specifications. In chap- ter 3 the KRI are defined, and they will be integrated in Chapter 4 as a fundamental part of the comprehensive model. Finally, Chapter 5 includes the results of the study ending with some possible further studies and additional considerations.

UNIVERSITÉ PARIS - EST
DOCTORAL THESIS
APPLIED MODELIZATION
TO ELECTRICITY MARKETS,
AS A FINANCIALLY
UNSTABLE COMPLEX
SYSTEM
Author: Supervisors:
Oscar MANCO LÓPEZ Dr. François LEGENDRE
Dr. Santiago MEDINA
A thesis submitted in fulfillment of the requirements
for the degree of Doctor in Economic Sciences
in the
Ecole Doctorale
OMI –“Organisations, Marchés, Institutions"
October 13, 2016iii
Declaration of Authorship
I, Oscar MANCO LÓPEZ, declare that this thesis titled, “APPLIED
MODELIZATIONTOELECTRICITYMARKETS,ASAFINANCIALLY
UNSTABLE COMPLEX SYSTEM” and the work presented in it are
myown. Iconfirmthat:
• Thisworkwasdonewhollyormainlywhileincandidaturefor
aresearchdegreeattheUniversitéParis-Est(Créteil).
• Where any part of this thesis has previously been submitted
foradegreeoranyotherqualificationatthisUniversityorany
otherinstitution,thishasbeenclearlystated.
• Where I have consulted the published work of others, this is
alwaysclearlyattributed.
• Where I have quoted from the work of others, the source is al-
ways given. With the exception of such quotations, this thesis
isentirelymyownwork.
• Ihaveacknowledgedallmainsourcesofhelp.
• Where the thesis is based on work done by myself jointly with
others,Ihavemadeclearexactlywhatwasdonebyothersand
whatIhavecontributedmyself.
Signed:
Date:v
“Anyonewhohasnevermadeamistake,hasnevertriedanythingnew.”
AlbertEinsteinvii
UNIVERSITÉPARIS-EST
Abstract
OMI–“Organisations,Marchés,Institutions"
DoctorinEconomicSciences
APPLIEDMODELIZATIONTOELECTRICITYMARKETS,ASA
FINANCIALLYUNSTABLECOMPLEXSYSTEM
byOscar MANCO LÓPEZ
Thechallengesfacedbydifferentsectorsoftheeconomy,respond
totheevolutionandspecializationofconsumersandproducers,where
the needs are becoming more complex. In this sense, during the last
5 years the electricity markets have undergone an evolutionary pro-
cess that aims to meet the needs of all stakeholders in the midst of
sustainabilityscenarios.
Thus,theagentsinvolvedintheelectricitymarket,presentanum-
berofexhibitionsofoperationalnature,legal,ethical,financial,among
others,whichrequireaspecializationallowingtheentryofnewtech-
nologies. This research project focuses on the study of financial risk,
which despite being so specific, consider many elements with the
aimofensuringthefunctioningofthemarketanditsparticipants.
In previous studies, some models have concentrated on the in-
vestigation of blackouts phenomena, the stability of the network,
the dynamic power system, and Smart grids, among others. Mean-
whileotherinvestigationshaveaddressedtheproblemofforecasting
different variables like the spot price and corporate strategy, with
the aim of increasing the profitability of the participants. Now, this
project presents the proposal of a complex financial model, which
results in calculating a market equilibrium considering initial condi-
tions and risk constraints. Using game theory it demonstrates equi-
librium instability and that through complexity it is possible to find
an optimal scenario in terms of profitability for the system and the
agents.
Inchapter1itcarriedoutareviewofpreviousstudiesinorderto
justifytheinvestigation,thenChapter2includesadescriptionofthe
Colombian electricity market, with different specifications. In chap-
ter 3 the KRI aredefined, and they will be integrated in Chapter 4as
a fundamental part of the comprehensive model. Finally, Chapter 5
includes the results of the study ending with some possible further
studiesandadditionalconsiderations.
Keywords: complex systems, game theory, optimization, KRI, finan-
cialrisk,profitability.viii
UNIVERSITÉPARIS-EST
Resúmen
OMI–“Organisations,Marchés,Institutions"
DoctorenCienciasEconómicas
MODELACIÓNAPLICADAALOSMERCADOSELÉCTRICOS,
COMOUNSISTEMACOMPLEJOFINANCIERAMENTE
INESTABLE
Oscar MANCO LÓPEZ
Los desafíos que enfrentan los diferentes sectores de la economía,
responden a la evolución y especialización de los consumidores y
productores, donde las necesidades cada vez son mas complejas. En
tal sentido, durante los últimos 5 años los mercados eléctricos han
sufridounprocesoevolutivoquebuscaatenderalasnecesidadesde
todoslosgruposdeinterésenmediodeescenariosdesostenibilidad.
Deestamanera,losagentesinvolucradosenelmercadoeléctrico,
presentan una cantidad de exposiciones de índole operativo, legal,
ético,financiero,entreotros,lascualesexigensuespecializaciónper-
mitiendo la entrada de nuevas tecnologías. Este proyecto de inves-
tigación se concentra en el estudio del riesgo financiero, que a pesar
de ser tan específico, considera bastantes elementos con el ánimo de
asegurarelfuncionamientodelmercadoysusparticipantes.
Endesarrollosprecedentes,algunosmodelossehanconcentrado
en la investigación de fenómenos de blackouts, la estabilidad de la
red, el sistema eléctrico dinámico, Smart grids, entre otros. Por su
parte otros estudios han abordado el tema de la predicción de vari-
ables como el precio y la estrategia corporativa, con el fin de incre-
mentarlarentabilidaddelosparticipantes. Ahorabien,ésteproyecto
de doctorado presenta la propuesta de un modelo financiero com-
plejo, que deriva en el cálculo de un equilibrio de mercado a partir
decondicionesinicialesyrestriccionesderiesgo. Utilizandolateoría
de juegos se demuestra la inestabilidad del equilibrio y a través de
la complejidad es posible hallar un escenario óptimo en términos de
rentabilidadparaelsistemaylosagentes.
Enelcapítulo1serealizaunarevisiónalosestudiosprevios,con
la intención de justificar la investigación, seguidamente el capítulo 2
comprende una descripción del mercado eléctrico Colombiano, con
sus diferentes especificidades. En el capítulo 3 se definen los KRI
que serán integrados en el capítulo 4 como parte fundamental del
modelo integral. Finalmente el capítulo 5 comprende los resultados
del estudio ejecutado con algunos posibles desarrollos posteriores y
consideracionesadicionales.
Palabras clave: Sistemas complejos, Teoría de juegos, Optimización,
KRI,Riesgofinanciero,Rentabilidad.ix
UNIVERSITÉPARIS-EST
Résumé
OMI–“Organisations,Marchés,Institutions"
DocteurenSciencesEconomiques
MODÉLISATIONAPPLIQUÉEDESMARCHÉSFINANCIERS
ENTANTQUESYSTÈMESCOMPLEXESET
FINANCIÈREMENTINSTABLES
Oscar MANCO LÓPEZ
Lesdéfisauxquelssontconfrontéslesdifférentssecteursdel’économie,
répondent à l’évolution et à la spécialisation des consommateurs et
des producteurs, dont les besoins sont de plus en plus complexes. À
cetégard,aucoursdes5dernièresannées,lesmarchésdel’électricité
ont subi un processus évolutif qui vise à répondre aux besoins de
tous les intervenants dans des scénarios de développement durable.
Aussi les agents impliqués dans les marchés de l’électricité, exposés
à des risques opérationnels, juridiques, éthiques, financiers, entre
autres, doivent ils se spécialiser pour s’approprier notamment de
nouvelles technologies. Cette recherche porte principalement sur
l’étude du risque financier tout à s’attachant à prendre en compte
les nombreuses spécificités des marchés de l’électricité dans le but
d’assurer le bon fonctionnement du marché et de ses participants.
Dans les développements antérieurs, certains modèles se sont con-
centréssurlesphénomènesdepannesdecourantélectrique,d’instabilité
du réseau, de variations de puissance, de réseaux intelligents, en-
tre autres. D’autres études ont abordé la question de la prédiction
de variables comme le prix et la stratégie d’entreprise, dans le but
d’accroîtrelesprofitsdesparticipants. Ceprojetdethéseproposeun
modéle financier complexe, qui se traduit par le calcul d’un équili-
bre de marché à partir des conditions initiales et des contraintes de
risque. En utilisant la théorie des jeux, nous expliquons l’instabilité
de l’équilibre. Nous montrons, en dépit de la complexité, qu’il est
possibledetrouverunscénariooptimalentermesderentabilitépour
le système et les agents. Ce travail est structuré de la façon suiv-
ante. Dans le premier chapitre, une revue des études antérieures
est présentée afin d’établir le contexte de la recherche. Le chapitre
2décritlemarchédel’électricitécolombienneavecsesparticularités.
Dans le chapitre 3, les indicateurs de risque (KRI) sont définis. Ils
constitueront une partie fondamentale du modèle complet présenté
danslechapitre4. Enfin,lechapitre5,d’unepart,présentelesrésul-
tatsobtenuset,d’autrepart,discutededifférentesvoiesd’approfondissement.
Mots-clés: Systèmes complexes, Théorie des jeux, Optimisation, KRI,
Risquefinancier,Rentabilité.xi
Acknowledgements
I would like to thank to professor François LEGENDRE for ac-
cepting to be the director of this dream and for their wise advices in
thisprocess.
Santiago MEDINA for having been a teacher and a friend since
longtimeagoandheencouragedmetostartthisamazingjourney.
Thanks to Oscar BOTERO for his important contribution in the
realizationofthisproject,andfortheracingbicyclesinParis.
Finally thanks to all the people who participated directly or indi-
rectly, friends,family, teachers andcolleagues. Eachof those present
orabsentnowadaysinthisadventure,whereresearch,emotionsand
writingprocesses,wereanexperiencewithchaoticcomplexity.xiii
Contents
DeclarationofAuthorship iii
Abstract vii
Acknowledgements xi
GeneralIntroduction xxiv
1 Electricity markets, game theory and complexity: State of
theart 1
1.1 Generaloverview . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Previousstudies . . . . . . . . . . . . . . . . . . . . . . . 2
1.3 Modelingofenergymarkets . . . . . . . . . . . . . . . . 5
1.4 Modelsusedformeasuringmarketperformance . . . . 7
1.4.1 GameTheory . . . . . . . . . . . . . . . . . . . . 8
NashEquilibrium . . . . . . . . . . . . . . . . . . 10
1.4.2 Agent-basedModeling . . . . . . . . . . . . . . . 11
1.4.3 Complexity . . . . . . . . . . . . . . . . . . . . . 13
ComplexSystems . . . . . . . . . . . . . . . . . . 16
Chaos . . . . . . . . . . . . . . . . . . . . . . . . 22
Selforganizedcriticality-SOC . . . . . . . . . . 23
1.4.4 Advantages . . . . . . . . . . . . . . . . . . . . . 24
2 Description: SituationofColombianelectricitymarket 27
2.1 Colombianelectricitymarket: review . . . . . . . . . . . 27
2.2 Operationoftheelectricitymarket . . . . . . . . . . . . 32
2.2.1 Generators . . . . . . . . . . . . . . . . . . . . . . 33
2.2.2 Transmitters . . . . . . . . . . . . . . . . . . . . . 33
2.2.3 Distributors . . . . . . . . . . . . . . . . . . . . . 33
2.2.4 Traders . . . . . . . . . . . . . . . . . . . . . . . . 34
2.2.5 Consumers . . . . . . . . . . . . . . . . . . . . . 34
2.3 Normativity . . . . . . . . . . . . . . . . . . . . . . . . . 36
2.4 Hiringenergy . . . . . . . . . . . . . . . . . . . . . . . . 36
2.5 RiskFactorsintheColombianMarket . . . . . . . . . . 37
2.6 Spaceresearchinelectricitymarkets . . . . . . . . . . . 40
3 KeyRiskIndicators: KRI 41
3.1 Generaloverview . . . . . . . . . . . . . . . . . . . . . . 41
3.2 Riskanalysis . . . . . . . . . . . . . . . . . . . . . . . . . 42
3.3 EnterpriseRiskManagement−ERM− . . . . . . . . . . 46
3.3.1 ClassificationsofEnterprisesRiskManagement 47xiv
3.4 Keyriskindicators(KRI)derivedfromcorporateman-
agementandwithapplicationtotheenergysector . . . 51
3.4.1 Macrokeyriskindicators . . . . . . . . . . . . . 52
Percentagedistributionofenergyportfolio . . . 52
Financialhedges . . . . . . . . . . . . . . . . . . 52
VARofenergyportfolio . . . . . . . . . . . . . . 53
Blackouts . . . . . . . . . . . . . . . . . . . . . . 53
3.4.2 Microkeyriskindicators . . . . . . . . . . . . . 54
VARappliedtothefinancialresults . . . . . . . 54
Earningsatrisk−EaR− . . . . . . . . . . . . . . 55
Operatingearningsatrisk−EBITaR− . . . . . . 56
DurationGAPbetweenassetsandliabilities−DGAP− 57
FinancialLeverage−FL− . . . . . . . . . . . . . 59
Returnoncapitalemployed−ROCE− . . . . . . 61
WeightedAverageCostofCapital−WACC− . . 62
Solvency . . . . . . . . . . . . . . . . . . . . . . . 64
Liquidity . . . . . . . . . . . . . . . . . . . . . . . 65
Indebtedness . . . . . . . . . . . . . . . . . . . . 67
Coverage . . . . . . . . . . . . . . . . . . . . . . . 68
3.5 Futureworksappliedtonewindicators . . . . . . . . . 70
4 ModelingElectricityMarketsfromacorporateperspective 73
4.1 Generaloverview . . . . . . . . . . . . . . . . . . . . . . 73
4.2 Firstapproximationtothephysicalphenomena . . . . 75
4.3 FinancialstabilityusingGameTheory . . . . . . . . . . 77
4.3.1 Optimization . . . . . . . . . . . . . . . . . . . . 83
4.4 Model for measuring systemic risk for energy agents:
Generalprocessandphysicalprocessusingacomplex
aproximation . . . . . . . . . . . . . . . . . . . . . . . . 84
4.4.1 AgentsProfit . . . . . . . . . . . . . . . . . . . . 88
4.4.2 Profit and losses statement: Representation of
thephysicalfinancialprocessfortraders . . . . 89
4.4.3 ConstraintsrelatedtoKRI . . . . . . . . . . . . . 92
Coverratio . . . . . . . . . . . . . . . . . . . . . 92
Indebtedness . . . . . . . . . . . . . . . . . . . . 92
Riskaversion . . . . . . . . . . . . . . . . . . . . 93
Financialleverage . . . . . . . . . . . . . . . . . 93
DurationGAP . . . . . . . . . . . . . . . . . . . . 93
EaR-EBITaR . . . . . . . . . . . . . . . . . . . . 94
Profitability . . . . . . . . . . . . . . . . . . . . . 94
Solvency . . . . . . . . . . . . . . . . . . . . . . . 94
4.5 Profitandlossesstatement: Representationofthephys-
icalfinancialprocessforproducers . . . . . . . . . . . . 95
Optimization . . . . . . . . . . . . . . . . . . . . 96
4.5.1 InBriefthemodel: . . . . . . . . . . . . . . . . . 97xv
5 Results presentation, comparison between methodologies
usedandexplanationoffinancialriskinterface 101
5.1 Generaloverview . . . . . . . . . . . . . . . . . . . . . . 101
5.2 Database . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
5.3 Resultsfromgametheorymodelation . . . . . . . . . . 103
5.4 ComplexsystemsResults . . . . . . . . . . . . . . . . . 110
5.4.1 ImplementationofRisKerplatform . . . . . . . 110
5.4.2 Agent’sdescription . . . . . . . . . . . . . . . . . 111
5.4.3 Optimization . . . . . . . . . . . . . . . . . . . . 117
5.4.4 RiskSituation . . . . . . . . . . . . . . . . . . . . 118
5.4.5 Comparison . . . . . . . . . . . . . . . . . . . . . 120
GeneralConclusions 123
A MatLabCode 127
B JuliaCode 133
C RiskerConstruction 135
Bibliography 139xvii
List of Figures
1.1 RandomWalk . . . . . . . . . . . . . . . . . . . . . . . . 13
1.2 Antbehavior . . . . . . . . . . . . . . . . . . . . . . . . . 15
1.3 Antbehavior . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.1 Operationalstructureforelectricitymarket . . . . . . . 30
2.2 Compositionoftheelectricitymarket . . . . . . . . . . 33
2.3 Functionsoftheelectricitymarketoperator . . . . . . . 35
2.4 Process of the modeling, financial vulnerability of the
electricitymarket . . . . . . . . . . . . . . . . . . . . . . 39
3.1 Exampleconsideringliquidity . . . . . . . . . . . . . . . 46
3.2 Intervalsforriskappetite . . . . . . . . . . . . . . . . . . 48
3.3 ProposalSchemeforEnterpriseRiskManagement . . . 51
3.4 Probabilitydistribution . . . . . . . . . . . . . . . . . . . 55
3.5 DistributionofEaRandEBITaR . . . . . . . . . . . . . . 56
3.6 Evolutionofdebtvs. profitability . . . . . . . . . . . . . 61
3.7 RelationshipbetweenWACCandcostoffundingsources 64
3.8 Solvency indicators in energy market in 2015 for the
mostimportantagents . . . . . . . . . . . . . . . . . . . 65
3.9 Categorizationbetweenliquidityandsolvency . . . . . 67
3.10 Coverage for principal agents in the Colombian en-
ergymarket . . . . . . . . . . . . . . . . . . . . . . . . . 70
4.1 Componentsthataffectsthecomplexityofthesystem . 75
4.2 Causesandeffectsoftheproblem . . . . . . . . . . . . . 76
4.3 SchemeoffictitiousAlgorithm . . . . . . . . . . . . . . 78
4.4 Visualizationofinteractionsituation . . . . . . . . . . . 80
4.5 Optimalfunctioningoftheenergysector . . . . . . . . 85
4.6 Differentlevelsforactingatthestockmarket . . . . . . 87
4.7 Proposedagent-basedmodelformodelingbehavior . . 88
4.8 Representationofinteractions . . . . . . . . . . . . . . . 95
4.9 Summarizedofthemodel . . . . . . . . . . . . . . . . . 98
4.10 Dutiesandresponsabilities . . . . . . . . . . . . . . . . 99
5.1 Utilityoptimization . . . . . . . . . . . . . . . . . . . . . 106
5.2 Resultsfor30agents . . . . . . . . . . . . . . . . . . . . 107
5.3 Resultsfor20agents . . . . . . . . . . . . . . . . . . . . 108
5.4 Resultsfor10agents . . . . . . . . . . . . . . . . . . . . 108
5.5 Resultsfor5agents . . . . . . . . . . . . . . . . . . . . . 109
5.6 Specificrelationships . . . . . . . . . . . . . . . . . . . . 112
5.7 Agentsanddemandchart . . . . . . . . . . . . . . . . . 113xviii
5.8 Agent’sinteractionsandcontractedprices . . . . . . . . 113
5.9 XM-Riskprofileforonerandomagent . . . . . . . . . 115
5.10 Riskscorecalculatedfromindicators . . . . . . . . . . . 115
5.11 Generaloverviewandgeneralriskpositionofthemar-
ket . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
5.12 Relativeimportance . . . . . . . . . . . . . . . . . . . . . 117
5.13 Interactions . . . . . . . . . . . . . . . . . . . . . . . . . 118
5.14 Graphicrepresentation: Allmarketinteractions . . . . . 119
5.15 Riskcomparisontable,salesdatabaseandsalesmodel . 120
5.16 Optimizinginteractions . . . . . . . . . . . . . . . . . . 120
5.17 Agent’sCoverage . . . . . . . . . . . . . . . . . . . . . . 121
5.18 Agent’sLeverage . . . . . . . . . . . . . . . . . . . . . . 121
5.19 RoceVs. Wacc . . . . . . . . . . . . . . . . . . . . . . . . 122
5.20 Agent’sDGAP . . . . . . . . . . . . . . . . . . . . . . . . 122
C.1 TestArchitecture . . . . . . . . . . . . . . . . . . . . . . 135
C.2 ProductionArchitecture . . . . . . . . . . . . . . . . . . 136
C.3 LandingPage . . . . . . . . . . . . . . . . . . . . . . . . 136
C.4 PlatformDashboard . . . . . . . . . . . . . . . . . . . . 137
C.5 Collapsed/ExpandedAgent . . . . . . . . . . . . . . . . 137
C.6 AgentsInteractions . . . . . . . . . . . . . . . . . . . . . 137xix
List of Tables
3.1 DGAP:Scenariosandsensitivities . . . . . . . . . . . . 59
3.2 NetAssets . . . . . . . . . . . . . . . . . . . . . . . . . . 62
3.3 RepresentationofIncomeStatement . . . . . . . . . . . 69
5.1 IncomeStatementforatrader . . . . . . . . . . . . . . . 103
5.2 Total demand and operations: most important agents
2015 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
5.3 ResultsDatabaseVs. NashEquilibrium . . . . . . . . . 105
5.4 ThresholdsforKRI . . . . . . . . . . . . . . . . . . . . . 114
5.5 Deviationscomparison. . . . . . . . . . . . . . . . . . . 122xxi
List of Abbreviations
ABM Agent-basedmodeling
ASIC AdministradordelSistemadeIntercambiosComerciales
CND CentroNacionaldeDespacho
CREG ComisiónderegulacióndeEnergíayGas
CROM Capacidadderespaldodeoperacionesenelmercado
DGAP DurationGAP
EaR Earningsatrisk
EBITaR Operatingprofitatrisk
EBIT Earningsbeforeinterestandtaxes
EBITDA Earningsbeforeinterest,taxes,depreciationandamortization
ERM EnterpriseRiskManagement
EV EnterpriseValue
FCF Freecashflow
KRI KeyRiskIndicators
MEM MercadodeEnergíaMayorista
NA NetAssets
NOPAT Netoperatingprofitaftertaxes
PPI ProducerPriceIndex
SOC SelfOrganizedCriticality
SSPD SuperintendenciadeServiciosPúblicosDomiciliarios
STN Sistemadeintercambioscomerciales
RWA Risk-WeightedAssets
UPME UnidaddePlaneaciónMineroEnergética
VAR ValueatRisk
WACC WeightedAverageCostofCapitalxxiii
Dedicated to my parents, Maria Ercilda and
Horacio, I’m here because of your patience. To
you because your presence in my life still
inspiring me. To my family and friends for
permanent support...xxiv
General Introduction
Energy planning is built from generation scenarios, marketing, dis-
tribution and consumption, which is still without a doubt the pro-
posed model by developed countries. In this regard the oligopoly
that comes inherited from ancient energy policies, has advantages
likethesupplyassurance,butagreatchallengeliesintheconcentra-
tionofrisk,thankstotheoperatingdiversityforeachregion.
In the particular case of generation, it is possible to find a variety
of forms of production, using fuels, clean energy, renewables, with
eco footprint, among others. Those energies determine the behav-
ior of oligopoly and by the way induce various types of risks that
compromisetheoperationindifferentmarketsandcountries.
Now, to establish what the consequences are, of exposure to dif-
ferent risks, sustainability becomes part of the discussions. All of
the consequences they sought to be avoided, for example consider-
ing international agreements that establish "binding" commitments
toreduceemissions. Thisleadsmanygovernments,tryingtochange
theirwaysofgenerationinordertomeetinternationalrequirements
andsustainability.
In this sense, sustainability may be the use of clean generation,
as much as possible. It can even define as how to use all renewable
resources in a coordinated manner. But it could also be the assur-
ance of supply with own resources, avoiding have recourse to the
international market regardless of the generation source. Even sus-
tainabilitycanbeframedwithinthepossibilityofbringingenergyto
anyoneintheworld,regardlessoftheway(Schiffer,2008).
Thatis,thereisnoprecisedefinitionforenergysustainability,the
same definition as when drawbacks are presented, still remains to
establishwhichpartofsustainabilityisunderthreat.
HowevertheWorldEnergyCouncil(WECforitsacronyminEn-
glish)definestheenergysustainabilityconsideringthreecriteria(Schif-
fer, 2008): First energy security, which aims to properly manage the
resources of a nation. Second, energy equity that is responsible for
ensuring the availability of supply for the entire population. And
finally the environmental sustainability, related to the use of renew-
ableenergyandthepossibilityofdecreasingthecarbonemissionsto
theenvironment.
Colombia is a particular scenario, thanks to the high concentra-
tionofgenerationbasedonnaturalresources(openlymeetsthethird
criterion), and it is not a great producer of emissions. However it
owesadebttosupplyenergytoallareasofthecountryfromthesec-
ond criterion (responsibility of the natural oligopoly). Finally with
respecttothefirstcriterion,themanagementoftheresourcesiscom-
promised considering the uncertainty that occurs during weather
events.xxv
More accurately, the power generation in Colombia with 70% in
hydrosourcestakingadvantageoftheavailabilityofnaturalresources
that it possesses. In other words, the energy is clean because it de-
pends less on fossil fuels, and the country is environmentally sus-
tainable. Nevertheless the operation of the system is delegated to
thecapacityofreservoirsorinotherwords,therainsareresponsible
fortheprofitabilityindicators.
Followingthis,howtomeasuretherisks,theintegrationandsub-
sequent interpretation is the focus of the different analysis in recent
times. TheforecastofBlackoutscenarios,inparallelwiththegenera-
tion portfolio optimization, maintenance plans and programming of
the ideal dispatch, conform a direct response to situations of uncer-
taintygeneratedintheelectricitymarket.
Nonetheless, having not yet conceived it holistically, all risks in-
volved in the energy context for the Colombian case. That is, today
itispossibletoquantifyrisksinanisolatedway,butitdoesnothave
tools to estimate the adjusted risk holistically, which produces sys-
temicevents,dominoeffectsorcascadetype. Thisriskisunderstood
as the instability of the system to internal and external events, to be
morespecific,currentmodelsdonotrespondtochaoticbehavior.
Chaos simply refers to a different order with respect to the tradi-
tional order; where various events are materialized and become in
inducers of a "domino" effect in which each piece trips the next one.
In the SOC methodology (Bak, Tang, and Wiesenfeld, 1988) they are
known as avalanches. (Bak, Tang, and Wiesenfeld, 1988; Bak and
Chen,1991)
Theseresultscomefromcomplexapproaches,whichareinherent
characteristics of the systems. There, the events that induce the be-
haviorcanoccuratanytimeandareinterrelatedthroughmathemat-
ical definitions. The events are intended to be simple but adjusted
descriptionsofphysicalphenomena.
The complexity can cause system instability if they do not have
tools associated with managing risk events, being this instability the
displacement of variables from its traditional area, that is a different
order to the common order. This allows us to affirm that for elec-
tricity markets where there exist many variables, is necessary the in-
corporation of innovative tools that allows the adequately manage
resources.
The energy market for most economies, represents a significant
proportionofGDP,andisresponsibleformaintainingtheproductive
machinery. Thus an event of inattention the supply, produces high
coststhatarenotquantifiedimmediately,forthatreasontheproposal
ofintegratedmodels,isattractivetointerestgroups.
Inbrief,tohaveinnovativetoolsformeasuringrisk,withtheaim
to make permanent controls and of course anticipate the events of
absenceorinattention,isimportantinordertonottoslowdownthexxvi
productivity of a country. Even though, understanding the physi-
cal phenomenon is a task that demands a level of abstraction that is
sometimes quite difficult. Although, it was unimaginable to think
that one physical phenomenon of an element in free-fall, could be
describedbyanequationwhichlaterwascalledgravity.
This research project highlights the complex benefits of electrical
systemsandfocusesspecificallyonthemicrofinancialsystem. Thus,
from a corporate approach, risk measurement is carried out consid-
eringtheisolationofinteractions,concentratingexclusivelyonbusi-
ness flows, where operating events don’t have representation. With
this, the results are obtained by generating a starting point, for fur-
ther integration with all physical phenomena identified in the dy-
namicsoftheelectricalsystems.
Nowadays, we can be witness and participate in the era of "com-
plex dynamics" where component integration undoubtedly, is look-
ingforwardtoanewwayofdealingwitheverydayproblems.1
Chapter 1
Electricity markets, game
theory and complexity: State of
the art
1.1 General overview
The electricity markets have undergone a transformation in recent
years,underthepretenseofoperatinginmorecompetitiveandprof-
itable environments. Thus in many economies around the world
it has gone from big monopolies to oligopolies, where competition
laws of supply and demand govern their behavior (Krause et al.,
2006).
On the other hand the experience of the agents involved in these
kindofmarketsareincreasingly,theirlevelofknowledgeoftheenvi-
ronment, and the facility for access to information, making the com-
petition more dynamic. Thus, more robust models for measuring
risk are required, allowing them to implement the planning of the
operationintheshortandmediumterm.
Eachagenthasdefinedobjectives,inmostcasesprofitmaximiza-
tionunderdifferentconstraintsofinternalorexternalcharacter(Gnan-
sounou et al., 2004). In this type of scenarios with open markets and
free competition, it is a very complex consideration of all the vari-
ables involved, however from different methodologies can be ap-
proximationstothephysicalphenomenathathappens.
One of the biggest complications is the exercise of predict the
demand, which is a critical variable for generating prices. To this
end there are plenty of models with the aim of establishing the best
strategy in the energy auctions, which optimizes the profitability of
generatorsbutexcludesincomefromtraderswhosemainfunctionis
brokeringwithadifferentriskexposure.
On the other side, with the aim of ensuring compliance of the
transactions, there are no mechanisms to assess the interaction of fi-
nancial performance between traders of coordinated manner (Zhou,
Chan, and Chow, 2007). This process is delegated to free market
movement, and is done partially or by studying the individual situ-
ationofeachagent,throughindicatorsthatnotreflectsthedynamicsChapter1. Electricitymarkets,gametheoryandcomplexity: State
2
oftheart
ofinteractions.
In that sense, the need for models to measure the performance
of financial affairs for the traders and generators is obvious. These
modelswillbeorientedtotheinteractionbetweenparticipants,their
complexity and severity if a difficulty appears. Thus, each partici-
panttake forwardastrategy tomaximizetheirreturns, whichisdis-
playedasapartofthesystemelementsoftheelectricitymarket.
It should be noted that in any market where commercial transac-
tions take place, regardless of the goods or services, uncertainty ap-
pearswithexternalandinternalnature,likeeconomical,operational
and financial, among others. This uncertainty will cause problems
that affect the stability of the markets if management and control
toolsarenotused.
That’s way in this research project we are focusing on develop of
a new tool for manage the corporate risk, considering the previous
studiesandactualtheoriesthatwedescribeinthefollowingsections.
1.2 Previous studies
Studies about electricity markets and their evolution have been di-
rected towards two major flows. First, the tendency to estimate the
market variables such as stock price, the price of contracts, demand
level, supply level, generation capacity, among others; by using sta-
tistical tools, mathematical formulation or even simulation. Second
calculating exhibits in the functional systems, in order to establish
with some certainty, the magnitude of the problems that fall within
theoperation.
In the results found by (Tushar et al., 2013) the equilibrium be-
tween supply and demand through the use of game theory, where
consumers play an important role in creating price, was the most
important advance. However, to maximize the profitability of the
consumer is an ambiguous result, because despite being located at
the end of the energy cycle, what which seeks user is the reduction
in the cost without generating returns through speculation or even
arbitrage,andcommonlyisnotthepurposeofthebusiness,itmeans
the consumers used the energy as the necessary good but not like
profitable(Borenstein,Bushnell,andKnittel,1999).
Forhispart(MedinaandMoreno,2007;Sweeting,2007;Wolfram,
1999) worked in the decomposition of the variables involved in pro-
cess of creating prices, including phenomena such as social affairs,
climatic, economic indicators, regulatory requirements, and others,
using mathematical techniques, statistics or new technologies, like
artificial intelligence. Such decomposition aims at a certain level of
confiability,projectingpricedevelopmentsinthefuture(Joskowand
Schmalensee, 1983). However one of the major problems that has
anymodel,independentofthemethodologyused,istheevidenceof1.2. Previousstudies 3
the “back testing" results, which commonly diverge of the observed
reality. Atthistime,wehaveuncertaintyandoperationalapproaches
In the same way, portfolio optimization tools are applied in the
generation of electricity (Stoft, 2002) and have gained importance
in recent years, allowing producers, maximize their profits consid-
ering the main sources of generation. In Colombia hydroelectric
generation considers almost 70.35% of total capacity (Sandoval et
al., 2004) leaving clear evidence of the exposure to climate phenom-
ena. Thus,generationusingalternativesourceslikesolar,thermalor
wind, have been winning gradually participation in the generation
portfolio, which allows having alternatives to ensure supply, based
on the recommendations from optimization techniques for energy
portfolios. Again we are talking about the operational situation of
the system, but just in few cases the intangible situation through fi-
nancialstudies,aredeterminedasaisolatedcontribution.
Continuingwiththedescription,studiesasdevelopedby(Aptet
al., 2004) have been trying to visualize the operational phenomenon
from the manifestation of blackouts that directly affect energy sup-
ply,withtherespectiveeconomicimplicationsofacountry. Inrecent
results achieved by (Apt et al., 2004) it can determine the possibility
of incurring losses due to the materialization of operational events,
such as impairment of physical transmission network, system fail-
ures, maintenance, changes in voltage, levels of risks, human errors,
weatherevents,amongothers.
Quantify risk exposures related to the operation, and financial
exposures linked to power generation have captured the focus of
the different works developed so far (Apt et al., 2004; Medina and
Moreno, 2007; Nanduri and Das, 2009). While the ideal scenario
is that the market remains in equilibrium, where agents maximizes
their returns with minimal transaction costs, and where the energy
supply is reached without incurring losses. But, there is another fac-
torconcerningtheadequatecapacitytomeetcontractualobligations,
thatis,ifindeedtheagentthathascommitmentshasatthesametime
thefinancialstrengthtohonorthem.
Inthiscontext,researchhasaddressedtheproblemofinteractions
between agents from a purely functional or operational perspective.
For(Aptetal.,2004;MedinaandMoreno,2007)itisevidentthateach
agent,trader,generatororconsumershouldestablishedtherelation-
ship level with other participants, looking for maximize the results
amid the laws of supply and demand, but the control of the finan-
cialexposureisanotherfactorwhichensuresthefunctionalityofthe
system. In other words the traders want to reach an equilibrium for
themandforthesystemingeneral.
The approach using game theory, has found results through the
integration of the decisions of the agents (Wiszniewska-Matyszkiel
etal.,2008). Also,agent-basedmodeling-ABM-aimstoexplainthe
phenomenon of interaction in order to engage in proper planningChapter1. Electricitymarkets,gametheoryandcomplexity: State
4
oftheart
to ensure the satisfaction of the demand (Weidlich and Veit, 2008).
Andagaintheproblemconsidersonlythefunctionalperspectiveand
the financial stability it is implicitly considered, like an assumption,
which always is fulfilled. Finance situation is despised, but is neces-
sary for the fulfillment of transactions the system, for this reason we
aretakingandstudyingdifferenttheoriestointegratethischaracter-
istic.
Abouttheresearch,theresultsfrommodelingbyusingABMcan
determine the evolution of energy prices based on direct or indirect
relations (LeBaron, 2005), simulate the dynamics to estimate the op-
timalenergyproduction(Young,Poletti,andBrowne,2014)toestab-
lishthebestalternativefornegotiation,consideringtheoremssuchas
marketpower(Krauseetal.,2006;LeBaron,2005)orevencontribute
in the management of Smart Grids (Apt et al., 2004) consolidating
informationfromeachparticipant,withthecorrespondingimpactin
the system. However, these studies again obey to the operational
performance of the market, and the possibility of explaining the op-
eratingphenomenonthathappens.
Having said this, it is increasingly evident the need to treat the
physicalphenomenonfromafinancialpointofviewamongthepar-
ticipants. Historically, some events of unmet demand have occurred
becausesomeagentsfacedproblemsinitsfinancialpositiontohonor
contractual obligations, even though the reaction is immediate by
the regulator (Minas, 2013). If there are presence of weakness in fi-
nanceaccounts,ispresentedthematerializationofrisks,wherecom-
mitments (covenants) can’t be honored without the operator of the
system can anticipate objectively the occurrence of any event of de-
fault, considering the financial information provided by agents and
thetransactionsinthemarket.
Thus,theconstructionofanintegratedmodelthatdeterminesthe
positions of financial risk of each agent, with their implications for
the market is justified from the point of view of securing the energy
supply and more specifically the assurance of the financial equilib-
rium which means the confiability of the market business. All pre-
sented theories are a good approximation to measure and integrate
thefinancialconditionsoftheagentsinscenariosoftransactions.
And the business of electricity has additional particularities, be-
causeoneofthemajorpremisesofthepowermarket,isthatdemand
has a passive position and the offer has an actively position (Med-
ina, 2006; Medina and Moreno, 2007). The last affirmation, shall be
deemed through the process of construction of the models, because
given the integration of the risks and the passivity of the demand,
this can’t be managed with existences, it means the agent can’t store
electricity like any merchandise. That’s why working capital and
liquidity have particular forms of treatment according to the risk fi-
nancialmeasure.1.3. Modelingofenergymarkets 5
In profitability terms, corporate profits are subject to the submis-
sion of tenders firm power and therefore the second step for partic-
ipants, is to present in detail its financial capacity and that of the
other actors involved to make transactions without compromising
businessviability.
1.3 Modeling of energy markets
A market dominated by a small number of service providers or pro-
ducers of products, is an oligopoly (Tremblay and Tremblay, 2011),
andtherearelimitationsinvolvedwitheachparticipant,evenifeach
knows the actions of their competitors in order to preserve the func-
tionality of the market. Similarly if one of the participants changes
the conditions of operation, the others must find out instantly be-
cause their returns are affected, decreasing competition from all the
system. In other words if a participant changes the rules, the others
mustreactimmediately.
In this context the energy markets are oligopoly because partici-
pants often pursue strategies, and adapted those strategies in order
to change the market conditions (Borenstein, Bushnell, and Knittel,
1999; Stoft, 2002). Also, the participants perform approaches, which
enable the functionality of operating models in a complex frame,
considering the large number of variables and situations to consider
(Borenstein, Bushnell, and Knittel, 1999; Yousefi, Moghaddam, and
Majd, 2011), because they need simulate the different scenarios. In
addition, each member of the oligopoly wants to maximize their re-
turnsonequitybyconductinggoodbusinesswiththeirpeers.
Gametheorycanrepresentthestrategicbehavior,however,many
of these models are very simple and do not capture the complexity
that comes from the markets, despite the fact the markets are bring-
ingpartialsignalsofthisbehavior(Stoft,2002). Butafterallfindings
and developments from this methodology, we can integrate Game
theory with other areas of knowledge in order to improve results.
All these theories seek to find a good solution in order to make pur-
chases and sales between agents in adequate way, considering the
financialrisk.
On the other hand, the agent based model - ABM - overcomes
some of the weaknesses of the model of market equilibrium central-
ized which represents the price formation, and the balance between
the competitors ensuring the stability of the system (Gnansounou et
al., 2004). where the main objective is the fulfillment of the demand
butfinallynotensurethefinancialviabilityofparticipants.
ABM models can represent heterogeneous individual agents and
their behavior, the rules of the market and the agent’s actions in a
decentralized manner (without central control). These models are
increasingly used to analyze the decisions made by the generators,Chapter1. Electricitymarkets,gametheoryandcomplexity: State
6
oftheart
distributors, traders, regulators and consumers in a liberalized mar-
ket(Zhou,Chan,andChow,2007).
In(WeidlichandVeit,2008)itisdoneacriticalreviewoftheABM
models for electricity markets and they found that most of the mod-
els focus on issues of market power and tend to ignore the restric-
tions of transfers in certain markets. The results found in (Yu, So-
mani, and Tesfatsion, 2010) propose the creation of a right in order
to obtain profits in congestion scenarios in transmission networks,
which allow the recognition of existence of over costs in a congested
network,i.e. asolutionofanoperationalcommonproblem.
However,thisproposalactsliketheresponsetoaninherentchar-
acteristictotheoperativesystem,andagainevadesthefinancialrela-
tionshipbetweenthegeneratorandmarketeroreventheinteractions
that consider the methodologies ABM and Game Theory, but from a
generalperspective.
Themodelsoftenignorethemarketdemandanswers,theimplied
characteristics in the evolution of prices and restrictions intervals in
the network (Medina and Moreno, 2007), and incidentally consider
thatsomeassumptionsarealwaysfulfilled,likethefinancialstability.
The development of a model ABM, which includes the behavior of
demand,priceandavailability,willallowprogressinunderstanding
howtheenergymarketsoperateandatthesametimetheinteraction
withnewtechnologiesandotherfactorsunderlyinginthemarket.
The construction of energy market models has focused on the
estimation of price developments, forecast of demand, simulation
of market strategies from producers agents, defining energy poli-
cies,technologyselection,amongothers(MedinaandMoreno,2007).
This is one of the major contributions of this work, because it is not
focused on the study of price hedging through derivatives, but on
maximizing returns through the consideration of the financial risk
of the agents. For this reason exploring the interrelationships of the
agents with the operation of the electrical system in the short and
medium term from the point of view of its financial strength, it is
somethingthatshouldbeexplored.
And it is important because the properties of an energy market,
includes immediate delivery, storage limitations, the inelasticity of
thedemandintheshorttermandthefulfillmentwiththeregulation,
which allows an agent based modeling - ABM. This methodology is
agoodapproachtounderstandthecomplexityofthesystem(Pakes,
2015), but should be treated in depth with the inclusion of interac-
tions between participants and their level of exposure to financial
risk,bytheway,creatingaspaceforresearch.
Themostimportantaspectofthisresearchprojectistheexistence
ofconceptualgapsintheprocessofmodelingelectricitymarkets,re-
latedtocorporateriskapproach. Financialriskfactorssuchascredit
risk;counterparty,operationalandmarketcanaffectthecompetitive1.4. Modelsusedformeasuringmarketperformance 7
position of the decisions of the agents and impacting the stability of
theelectricitymarket.
Considerations as macroeconomic issues, financial and solvency
typeareelementsthataffecttheperformanceoftheagents,theirmar-
ketshareandgenerateadministrativeactionsbythesystemoperator.
It is possible wondering about how to measure the vulnerabil-
ity of the system agents in front of financial risk factors and how it
affectstheoperationofthemarketasawhole. Sinceforsucheventu-
alities, there may be episodes of unmet demand, which leads a high
opportunity cost, and in the other hand the impact suffered by the
national economy that aims to make of opening to global markets a
boosttoeconomicgrowth.
1.4 Models used for measuring market per-
formance
The inclusion of processors to perform calculations from the decade
of the 60’s was of vital importance to achieve results in record time
fromsimulationprocessesanditeration. TheXXIcenturycamewith
importantadvancesfrommathematicsthatpurportedtodescribethe
operationofphysicalphenomenagivingspacetostrongresearchand
development(Kwapien´ andDroz˙dz˙,2012).
Among the advances, game theory began as a methodology that
sought to respond to the economic phenomena of interaction be-
tweenparticipantsinasystem(LeBaron,2005).
Thefirststudieswereconcentratedondescribingmathematically
astheprocessofdecisions,evolvesinperfectenvironmentsofknowl-
edge among participants of the process (Medina and Moreno, 2007).
In turn, further research evolved into a complex mathematical lan-
guage, giving way to new definitions of philosophy that openly ex-
ceededtheinitialproposals.
Moreover, agent based modeling (ABM) emerged as a promis-
ing method to advance the understanding of the systems under dy-
namic conditions (Fischer and Riedler, 2014). The inclusion of that
methodologyallowedtheevolutionofeachelementandlevelofim-
pact through integrated models, achieving easily understand oper-
ation for management and control resulting from the integration of
thecomponentsusingequations.
Indeed,electricitymarketsareexperiencinganumberofconstraints
and uncertainties when executing investments because of the situa-
tion of weather and climatic changes. Each decision maker is au-
tonomous, and requires preliminary information that incorporates
the ability of agents to interact, communicate and negotiate with
eachother. Theagentbasedmodelingprovidesthispossibility(Gnan-
sounou et al., 2004) and also to simulate individual situations that
enrichtheanalysis.Chapter1. Electricitymarkets,gametheoryandcomplexity: State
8
oftheart
The agents are autonomous, distributed in a system and are “in-
telligent", i.e. that they are communicative, rational, adaptive and
they learn (Gnansounou et al., 2004), characteristics which becomes
inthemaincontributionofagent-basedmodeling.
Similarly, the complexity helps to establish more structural way
each of the taken decisions considering the inclusion of chaotic be-
havior and the butterfly effect (Costa et al., 2007). The complexity
comes in a system consisting of interrelated parts, which together
generateresultsnotsoevident(Costaetal.,2007).
Complex systems usually are not as complicated systems, be-
causeitsintentionistobeasimpleexplanationofphysicalphenom-
ena;inthisregardwecananalyzeandfindtheelementsthatproduce
complexbehaviors.
Andfinally,oneofthegreatcontributionsofthecomplexdynam-
ics is that we can define mathematically the interactions among par-
ticipants, the type of operations that have each other, and the kind
of relationship useful for determine through equations of first and
second degree the level of complexity (Costa et al., 2007; Newman,
2003). Thus physical phenomena are reduced to mathematical ex-
pressions in sets of soluble real numbers. In the next section we in-
troduce the generalization of game theory as one of the main meth-
odstostudytherelationshipbetweenagentsandtheirinterrelations
throughstrategies,aspartofthefinancialrisk.
1.4.1 Game Theory
Game theory was born as a mathematical methodology applied ini-
tially in problems with economic nature and is based on strategies
that are taken from what is estimated will be the decisions of others
(Gibbons, 1997). Each participant in the process has access to certain
information,whichwillallowmanagingtherisksandhowtheywill
taketheirdecisions.
Agameisamathematicalrepresentationthatincludesstrategies,
actions, number of participants (these may be individuals or organi-
zations),probabilitiesandprofitability(NeumannandMorgenstern,
1947). Thus there is an interdependence that involves each of the
players (agents) in the decision process and the decisions that they
takewillaffectothers.
The combination of strategies to improve the profits of the par-
ticipants, will be understood as a equilibrium in the game, although
it will be static while initial conditions do not change (Agarwal and
Cui,2012),inthissenseitisimportanttonotethatstaticconditionis
oneofthebiggestproblemsofgametheory,giventhattheinitialcon-
ditions of the systems are evolving constantly. In electricity markets
such conditions are dynamic because every certain period is neces-
sarytoestablish,whichagentscandobusinessornot.1.4. Modelsusedformeasuringmarketperformance 9
Similarly,themodelingoftheelectricitymarketasagamesearches
toachieveresultsmaximizingprofitsforeachoftheparticipantscon-
sidering initial conditions. A further problem is that this approach
assumesathoroughunderstandingofthecharacteristicsofeachpar-
ticipantandfromafinancialpointofviewisdifficulttoestablishthe
planningofallsystemelements.
Theelementsofagameare(Gibbons,1997):
• Players (N): individuals who have to make decisions, always
assuming that seek to maximize their utility, in the case of en-
ergymarkets,theagents.
• Actions (X): possible alternatives that a player can take at any
moment where it should decide, e.g. buying and selling deci-
sionsintheelectricitymarket.
• Information: degree of knowledge that is available at all times
foreveryone,aboutthevaluesthattakedifferentvariablesand
statusofotherparticipants.
• Payoffs(U):representsthevaluereceivedbyplayersattheend
of the game as a profit, in this case the net profit after interest
forelectricitymarketagents.
• Equilibrium: set of strategies that players take for play the
game, searching the optimizing the payoff function (profit) in
frontofothers. (Neuhoffetal.,2005)
The mathematical expression of a game is presented as follows (Ca-
chonandNetessine,2004;Gibbons,1997):
G = [N,X ,U ] ∀i = 1,2,3,...,n
i i
Players: N = 1,2,3,...,nisafinitesetofn,indexedbyi. Setofactions
fortheplayerix
i
x =(x ,x ,...,x )inthecaseofelectricitymarket,thissetconsider
i 1 2 n
purchases and sales of energy, defined in quantity of energy traded
(i.e. kwh).
Utilityfunctionor“payoff"forplayeri: U
i
U = (u , u , ..., u ) is a profile or functions of utility (Gibbons,
i 1 2 n
1997;Tusharetal.,2013)
The most important assumptions of game theory, according to,
(LIandLIN,2013)are:
• Allagentsareinterestedintheirownambitions.
• Eachagenthasautilityfunction.
• The preferences of each agent can be described by the utility
function.Chapter1. Electricitymarkets,gametheoryandcomplexity: State
10
oftheart
• Everyagentknowsthepossibleactionstakenbytheothers.
.
From the foregoing, game theory is emerging as a useful tool for
describing various phenomena in the markets, despite the fact that
theassumptionsfortheirimplementationarequiteidealists. Onthis
basis it is possible to define strategies in different environments that
enable it to be the best response to competitors giving way to the
calculation of the equilibrium, which speaks of profits in competi-
tive environments and is the best strategy on the part of the partici-
pants.TheNashequilibriumisthefirstapproximationwhenwehave
many payoffs with different goals from agents, the idea is to find an
idealscenariothatconnecttheperformanceandthestability.
NashEquilibrium
Itispossiblecalculateit,inenvironmentsofperfectcompetition,but
thefinaldecisionsdonotconsiderthelikelyreactionsofrivals(Gatti,
Rocco, and Sandholm, 2013; Gibbons, 1997). This because such de-
cisions associated with any of the participants will have a negligible
impact on market behavior that can be discriminated. The most im-
portant task of the participants is to anticipate market behavior and
howtomaximizeprofits(Stoft,2002).
Thatsaid,themeasurementproposedby“Cournot"initscompe-
tition model (Day, Hobbs, and Pang, 2002; Dekel, Siniscalchi, et al.,
2014; Tushar et al., 2013) can be adapted, because for the electricity
marketinthefirstphase,companiescompeteforpowercapacitythat
can be produced, while in the second phase, companies compete for
theamountofenergythattheycantrade.
In the Nash equilibrium each participant knows which is its best
strategy taken, and all participants known the strategies of others
(Day, Hobbs, and Pang, 2002). It can also be understood as a har-
monyinwhichachangeofstrategydoesnotputtheagentinaposi-
tionofadvantageovertheirprofits(Gibbons,1997).
The main problem is that for achieve the equilibrium does not
existsimplecalculationtoolswhentherearealargenumberofagents
withdifferentstrategies.
When the game has many agents, the equilibrium can be ap-
proached by two methods, first the fixed - point and second in the
caseoffinite-dimensionalmultilinearpayoffstheauthors(NlKAIDO
andIsoda,1955)havebeenworkedinthesolutionoftheproblem. In
thisresearchproject,weconsiderthesolutionwithdifferentpayoffs,
because that depends on the financial size of the agent, it means a
complexgamewithmultilinearpayoffs.
Theelectricitymarket,therefore,operatesasanoligopolyconsid-
ering the generation process because in Colombia there are few big
generators, and some strategies are previously known in the busi-
nesschain.1.4. Modelsusedformeasuringmarketperformance 11
Forexample,theproducerwillmaximizetheirprofitsbyproduc-
ing more energy than usual in the absence of climatic, operational
orexternalevents,althoughsubjecttorestrictionsbytheregulatorof
thesystem,associatedwiththeinstalledcapacityandthesatisfaction
ofdemand.
Traders know the strategy who was chosen by generators and
they make purchases of energy through bilateral contracts in order
to hedge against the existing volatility in demand and inside of the
creationofprices,inturnsuchdecisionsarebeingevaluatedconsid-
eringlocalandinternationaleconomicconditions.
Theprisoner’sdilemmaisanexample(Alos-FerrerandAnia,2003;
Buttler and Akchurina, 2013; Gibbons, 1997) which runs between
agents descriptively but only for two participants. However, the
Nash equilibrium occurs when traders, consumers and power gen-
erators that are part of the global market, have adequate energy ex-
changes, so that the returns and profits are under acceptable levels
ofriskaversion,butthisisnotsoobviousasafinalsolution.
Mathematically,Nashequilibriumcanbedefinedasfollows: (Gib-
bons, 1997; Heusinger, 2009): If each agent knows what everyone
else will go to do, it would be easy to pick its own action and in this
terms optimize its profitability function, i.e. the player (agent) does
nothaveargumentsforchangethestrategy(Heusinger,2009).
With,
U = (u ,u ,...,u )
i 1 2 n
Andalso,
x = (x ,x )
i −i
Then,
U (x∗,x∗ ) ≥ U (x ,x∗ ) ∀x ∈ X
i i −i i i −i i i
Thismeansthatx∗isthebestresponsethatisthebeststrategyagainst
competitorsoragentstomaximizetheirprofits.
1.4.2 Agent-based Modeling
For many years the research question posed from different areas of
science,focusedonhowtodescribethecharacteristicsofparticipants
in a system and their relationships (Yao, Adler, and Oren, 2008).
Agent-based modeling (ABM) has become a useful tool to approach
the complexity of the interactions between the elements of the sys-
tems and the methodology has begun discussions about the degree
of difficulty with which each system should be treated with their re-
spectivepeculiarities.
However, describe phenomena that explain the relationship be-
tween the agents through equations is quite complex (Zhou, Chan,
and Chow, 2007), i.e. it is not a simple process because the consider-
ation of all characteristics through a single mathematical expressionChapter1. Electricitymarkets,gametheoryandcomplexity: State
12
oftheart
in a linear or polynomial way can be sometimes a simplistic expla-
nation of physical phenomena. However one of the main objectives
is to explain by simple equations, the complex reality, which is that
partofourjobasresearchers,whichistosimplifyrealitythroughthe
results.
Similarly evolutionary systems with self-learning, independents,
withhighorlowdynamic,amongotherthings,arecollectingcertain
relationshipthatisnoteasytointerpret(Newman,2003).
Thefinancialandeconomicfieldisnostrangertothephenomenon,
as it considers certain characteristics typical of ABM. That was how,
in the early twentieth century when models like the CAPM for the
allocation of capital assets, the Sharp model for determining opti-
mal portfolios, the “Black - Scholes" model which applied stochastic
concepts on financial options and overall classical financial theory
derived of concepts of Alfred Marshall (Humphrey, 2004), among
others. Theywerenothingmorethantheresultsofconsidertherela-
tionsbetweenelementspresentinthemarketsthroughequations.
Inthatway,therearemanycomponentsconsideredaboutthede-
scription of the physical phenomenon (equations). For this reason,
the reliability of the estimates has been compromised for long time.
Such is the case of the success of the "Black Scholes" model for op-
tion pricing in the early 90’s and the subsequent bankruptcy of the
investmentfundmanagedbytheircreators(Greenspan,2007).
This,becauseattheend,theresultsoftheequationsmaypartially
explain the phenomenon or not, and the explanations of the failures
is they do not consider all the variables involved. Then, the theo-
retical frameworks started to talk about heterogeneous subsystems,
and those advances makes the descriptions and further analysis are
criticalandmoreadjusted(Kuznetsova,2014).
An example that sums up this phenomenon is the hypothesis of
efficientmarketsproposedbyEugeneFamainthe60’s. Inthetheory,
the behavior of financial markets is simplified through the ability to
predict future prices using one equation with different assumptions
(MalkielandFama,1970):
Y = µ +(cid:15)
t t
This formula is a reduction of phenomena occurring around pre-
dictions of future prices. However, the “random walk" continues
being a relevant theory as a starting point for assumptions and sim-
ulations of financial process. While the expression is quite simple at
least in mathematical terms, today remains a benchmark for under-
standingthemechanicsoftheagentscrossingtransactionalinforma-
tion in the financial markets, even though many of the assumptions
aredifficulttofulfilled.
The Figure 1.1 present a generic evolution that can be estimated
from historical data stored, however there are a lot of variables in-
volvedintheforecastingprocessthatarenotconsidered.1.4. Modelsusedformeasuringmarketperformance 13
FIGURE 1.1: RandomWalkExample
Continuing with the task of explaining the physical phenomena
usingformulas,ifeachoftheagentsinvolvedinthefinancialmarket
(investors, issuers, regulators, intermediaries, etc.) has similar be-
havior,describedbytheequationofrandommotion,thentheaggre-
gationofeachofthesebehaviorscouldyieldcomprehensiveincome
around the market, nevertheless, model the behavior of the partici-
pantsbymeansofequations,isnotanobviousprocess.
There are differences between classical modeling and the pro-
posalthatcomesfromABM,themostimportantaccordingto(Batty,
2007)areasfollows:
1. Classicalmodelsconsideronlyoneagentthatrepresentsallthe
agentsofthesystem;byotherpartABMestablishesthatagents
of the system are simplified in an equivalent number of agents
inthemodel.
2. Intheclassicalmodelsthereareconditionsimposedtothesys-
tem: trend to disequilibrium, trend to minimum values more-
over,ABMrepresentsinteractionsbetweenphysicalagents,con-
sideringinteractionrulesandinitialconditionsthatcanchange.
Now the complexity is presented in order to connect more ele-
ments to describe the physical phenomenon of financial risk. In this
case,theaimistointerprettherealitywhenagentsmaketransactions
betweenthem.
1.4.3 Complexity
A system is a combination of different logical or even physical en-
tities that interact with each other to establish a specific purpose,
namely to reach a target from the relationship between them (Solé
and Manrubia, 2009). The systems can be dynamic, and it means
thatbehaviorchangesovertime,orthesystemscanbestable,where
the conditions, generally do not change and remains in equilibriumChapter1. Electricitymarkets,gametheoryandcomplexity: State
14
oftheart
(Boccara, 2010). In the chapter 4 we use this definition in the con-
structionofthegeneralmodel.
The complexity meanwhile, as defined by (Solé and Manrubia,
2009) can be understood as the level of difficulty with which we can
predict the behavior of a variable or an overall system, thanks to its
internalcharacteristicsandtheirrelationshipwiththeenvironment.
Similarly after setting the behavior of those variables or systems,
with the respective interactions, it is possible to determine that be-
haviorscanbesimpleifthecomplexoriginsareclearlyidentified.
The integration of complexity and systems for their part, allows
thecompositionofsystemswithmanyparts(orvariables),withmany
degreesoffreedomthatarenotequivalentbetweenthem(Levy,1994;
Tumminelloetal.,2005)meaningthateachelementisindependentin
making their decisions and governed by different parameters (Tum-
minello et al., 2005). That said we could define complexity as the
study to determine how complex systems can generate simple be-
haviors (Solé and Manrubia, 2009) but only if the origin of complex
situations is understood, in other words if the physical phenomena
arecompletelycomprehended.
A physical phenomenon according to the chemical theory, are
those transformations in a body that does not change the nature of
matter of which this is constructed, for example, rain, wind, elec-
tric power transformation in motion (Stavridou and Solomonidou,
1989). And these phenomena can be transferred to other sciences,
such as economic phenomena that are associated with the activities
ofindividualsseekingthetransactionofgoodsorservices.
At the same time, there are countless examples that can be cat-
egorized as a complex studies, within which stands out: The oper-
ation of a vehicle, with many independent components related and
how they make the movement rolling in the street; a swarm of bees
where each participant has defined functions and all of them seek-
ing survival; or even one complex situation could be the life itself
(Tesfatsion, 2003; Tumminello et al., 2005). The human body has dif-
ferentphysicalcomponentsthatseekthesurvivaloftheorganism,if
acomponentfails,thesystemcouldcollapse.
Ants, for example as shown in figure 1.2, have a complex behav-
ior because each member performs activities defined by natural se-
lection (Boccara, 2010) and do not require a central control to ensure
thefunctioningofthesystem(theantcolony),itmeansthequeenlet
eachmemberdothejob. Inadditiontotheabove,suchsystemsben-
efits from the self-learning as a defense mechanism against possible
futureinstability.
Acompanyisbydefinitionacomplexsituationasitiscomposed
of different elements, such as fixed assets, intangible assets, employ-
ees,customers,suppliers,investments,intellectualcapital,sharehold-
ers,amongothers.1.4. Modelsusedformeasuringmarketperformance 15
FIGURE 1.2: Antbehavior
Each of these elements is integrated together to perform a com-
plete and complex function, which turns out to be the financial vi-
ability of the company and its sustainability (Yang, Gu, and Zhou,
2015).
Similarly,ifoneoftheelementsofthebusinessfails,thenthesta-
bility of the system is compromised and hence its future functional-
ity, namely if in certain case of affectation in the productive assets,
clearlytherewouldaffectthecorebusiness.
Inlinewiththeabove,ifacompanyseenlikeaunitcanbeclassi-
fied as a complex situation, a group of companies that interact with
eachotheralsowillbe. Suchisthecaseoftrademarketswheretrans-
actionsdeterminethedegreeofrelationshipbetweentheparticipants
(Jiang,Chen,andZheng,2014),whichthereforeseekthesustainabil-
ity of the system in the long term, ensuring their preservation and
profitability.
If one of the elements of the system presents problems for conti-
nuity,viabilityiscompromisedtoagreatorlesserdegreedepending
ontherelativesizeoftheaffectedagent.
By comparison, if a trade market presents complexity, it is more
difficult to estimate the generation of profits consolidated compared
with the estimate of profits for a specific company. However, from
this research project it is possible approximate the interactions be-
tweenparticipantsandthedynamicsoftheirprofitstointegratethem
laterfromtheperspectiveofcomplexdynamics(Boccara,2010;Levy,
1994), allowing approach from the actual view to economic viabil-
ity of the whole system, involving financial risk susceptibility fromChapter1. Electricitymarkets,gametheoryandcomplexity: State
16
oftheart
agents.
Since the liberalization of international markets with globaliza-
tion and access to information, it is necessary ensure the operation
ofenterprisesincompetitiveenvironments,independentifitsroleis
as a production company, service provider, public or private. Thus,
control of its financial performance makes them to assimilate evolv-
ing global challenges, and allowing interaction with the environ-
ments to become a dynamic system (Jiang, Chen, and Zheng, 2014;
Yang,Gu,andZhou,2015;Wyman,2011).
As we mentioned, to determine the level of profitability from the
systems, it is easier to measure individually instead of collectively.
However, there are studies where is more useful make a measure-
mentofreturnsintegratedandthenreduceittotheindividuallevel,
inthissenseappliedresearchoncreditriskusingdynamiccomplex-
ity can taste this relationship (Jiang, Chen, and Zheng, 2014; Yang,
Gu,andZhou,2015).
Theresultsfoundin(Yang,Gu,andZhou,2015)createascenario
for future research on financial problems, economic and risk, where
itispossibletounderstandthecomplexityoftheirindividualresults
ontheoverallperformance.
ComplexSystems
In a beehive, whose functionality is subject to the work performed
byeachindividual,itcanbeprovethatthetotalofthemembersper-
formedtheirroleincertaintasksconsideringtheircondition.
Itmeansthatbeesareclassifiednaturally. Gordon(Boccara,2010)
pointedoutforexample,thatforantcoloniestheassignmentoftasks
is a continuously adjusted process, in other words, independent of
the role executed by each ant either physical work, military, pro-
curement of food, cleaning, among others, all the distributions are
reviewedperiodically.
Ants permanently adapt to the situation without having a super-
visory figure to fulfill their duties. In other words there is no central
control, the queen does not decide who does (Boccara, 2010), allow-
ing the generation of a very proper emergent behavior of complex
systems.
There are many examples of complex systems behavior, among
which we can highlight the urban transport network, where each
participant can be classified as a member of the system; a company,
given the interactions among members of the organization and sub-
sequentguidancetoachievetheobjectives(Levy,1994);thetelecom-
municationssystems,beinginterrelatedthroughadatatransmission
network;theeconomy,thankstothehighneedtoconsideranumber
of variables to maintain a nation under budgetary control; among
others.1.4. Modelsusedformeasuringmarketperformance 17
The definition of a complex system comes from different disci-
plines such as biology, ecology, game theory, philosophy and others,
which historically have tried of modeling the relationship between
each of the components of the systems, or agents and its subsequent
integration through mathematical descriptions. The main features
for existence of complexity in a system according to (Boccara, 2010;
SoléandManrubia,2009)are:
• Existence of a large number of agents (individuals) that inter-
act.
• The self - organization of collective behavior, which makes dif-
ficulttoanticipatetheknowledgeofthebehaviorofeachagent
inthefuture(stateofemergency).
• The emergent behavior is not the result of the existence of a
centralcontrol,butratheroftheself-learning.
Theagentsarethenvitalpartofthesystems,andtheyhavediffer-
entfeaturesamongwhichstandsoutitsabilitytointeractwithone’s
environment and that they can respond to what happens around
them despite the existence of a stated purpose or not (Boccara, 2010;
SoléandManrubia,2009).
Asetofagentsformsanorganizedpopulation,forexampleinthe
caseofbees,thehiveiscreatedandinthecaseoftheexistenceofbuy-
ers and sellers the market is created. For purposes of this research,
power generators, transmitters, distributors, traders and consumers
arepartoftheenergymarketasaglobalsystem.
Subsequently, the populations organized in turn grouped all the
learningfromagentsandtheirautonomyandthestrategiesthatthey
taken as a way of responding to the environment, and if the strate-
gies are aggressive or otherwise passive (Tumminello et al., 2005), it
meanstheselflearningcanimprovethesurvivorofthesystemorlet
itfail.
As already mentioned, systems are a set of populations where
agents applied their strategies (Boccara, 2010) using the tools that
theyhaveandamidexternalconditions. Thecomplexityariseswhen
therearemanyinterrelationshipsbetweenelements,sothatthechange
inthestrategiesoftheagentscanaffectthebehaviorofthesystemin
thefuture.
In financial terms, a default of one of the agents involved in the
energymarkettransactions,cantriggerproblemsinthesystem,thanks
totransactionsthattheyhavebetweenthem,increasingtheprobabil-
ityfordemandwillbeunattended.
In the literature, it is possible to find two classifications for sys-
tems, if they contain populations seeking to adapt to the environ-
ment are called complex adaptive systems, but when several popu-
lations of agents adapt to each other the result is a system co - evo-
lutionary, and the system self-learns from experience (Boccara, 2010;Chapter1. Electricitymarkets,gametheoryandcomplexity: State
18
oftheart
Solé and Manrubia, 2009; Tumminello et al., 2005) it means improve
theperformanceconsideringtheevolution.
In the case of electricity markets, thanks to the operation itself,
eachpopulationgroup(traders,generators,transmitters,consumers)
performs the same activities and evolves based on the optimization
ofitsresults,referringtomaximizeprofitsbutatthesametimereach-
ingtheminimizationofthetotalrisk.
There are three elements required to understand the complexity,
which are: variation, interaction and selection. Variation is the main
component of the adaptation of the system given that it is necessary
to find a balance between uniformity and differentiation (variation)
so as to make easier propose solutions to those agents that do not
conformtotheaverageinyourbehavior(Boccara,2010).
Ontheotherhand,interactionreferstotheelementsrelated,when
and how, under the conditions set. This interaction is not always
symmetrical, much less uniform; it can be very intense (high re-
lationship) or diffuse (low relationship) (Solé and Manrubia, 2009;
Tumminello et al., 2005). It is clear that for electricity market agents,
interactionsarepresentthankstothecashflowsexchangedbetween
themconsideringpurchasesandsalesofenergy.
In this sense, it will be intense interactions when flows will be
high, where the amount of contracted energy is large (large number
ofbilateralcontracts)andwillbediffusewhentheamountofenergy
exchange be low or non existent, it means when they doesn’t have
businesseachother.
The third element is the selection, which refers to agents which
shouldbereplicatedandwhichshouldbeeliminated(Boccara,2010)
not only through the process of natural selection but rather because
ofthequalitiesthatcantransmittootheragents,usingdecisioncrite-
ria that are concentrated in cost, time, benefits, among others, or for
thepurposesofthisresearchproject,therisklevel.
From the point of view of financial risk, an agent that sees their
income statements compromised can incur in events of default and
maybeitcan’thonortheircommitments,subsequentlyaffectingother
agents for non-payment. This project proposes the identification in
advance of such event risk with the aim of reducing problems in the
operation of the market, and ensures the financial functioning of the
system.
The figure 1.3 shows a vectorial behavior regarding diversity of
agents involved in the system, the result after the processes of vari-
ation, selection and interaction converge to equilibrium considering
initialoperatingconditions.
It is important to talk about models that describe the complexity
mentionedabove,andforsuchpurposesthemathematicaltoolspro-
posed by (Boccara, 2010; Tumminello et al., 2005). are a solution to
this problem. Although there are a number of essential elements in
each system, this does not ensure that under the mathematical rules1.4. Modelsusedformeasuringmarketperformance 19
FIGURE 1.3: Convergencein2dimensions
Source: (Boccara,2010)
arenecessarilyconsidered. Theyshouldcontemplateonlythefactors
thoseneededtodescribeandunderstandthephysicalphenomenon.
Modelsmustbesufficientlycomplextocapturealltherelevantchar-
acteristics,butalso,simplesconsideringonlykeyissues.
On the other hand, a dynamic system begins to respond to ques-
tions about how to relate to the participants and the particularities
(Solé and Manrubia, 2009). Physical phenomena can be described
by equations where each solution is determined by the initial condi-
tionsfedintothesystem,resultingrelationshipsbetweenagents. For
its part, the description of evolution, its adaptability, the factors nec-
essary for the administration and decision-making will be results of
thecomplexitylevelfordescribingthephenomena(Tesfatsion,2003).
Therefore,theelectricitymarketconsiders,manyofthecharacter-
isticsofcomplexdynamic. Itmeans,theinteractionsbetweenagents,
self-learning, the selection of the best-positioned participant and the
ability to adapt to evolving environment. Those characteristics are
crucial to the formation of prices and ensuring energy supply, as
long as no commitment of system operation. In other words and for
the purposes of this research project, the system is stable, if financial
risksarenotpresent.
In general, complex systems are autonomous systems of differ-
ential equations that are based on dynamic characteristics (Solé and
Manrubia, 2009). Meanwhilea dynamicsystem is onein whichtime
does not appear explicit in the derivatives that confirm the relation-
shipsbetweenvariables,andisexpressedintheform(SoléandMan-
rubia,2009):
dx
= F(x(t),µ)
dtChapter1. Electricitymarkets,gametheoryandcomplexity: State
20
oftheart
Here time is only implicitly represented among the variables. In
other words an equation is linear if the function F appears in terms
ofconstantsandvariableswheretheydependofmultiplicativeterms
(Boccara, 2010). Thus a system is autonomous and linear if it is ex-
pressedasfollows(SoléandManrubia,2009):
x∗ = Ax
WhereAisamatrixofconstants. explicitly:
    
x∗ β β ... β x
1 11 12 1n 1
x∗ β β ... β x 
  . . .2  =   . . .21 . . .22 ... 2 . . .n     . . .2  
    
x∗ β β ... β x
n n1 n2 nn n
It is possible to solve the system and find the behavior of this
system,consideringsomeinitialconditionsinthephasespace(space
where the elements contemplated the possible states of the system)
that belongs to the system itself (Boccara, 2010). It means different
solutionsdependingondifferentinitialconditions.
However, given that the purpose of this research project is not
toproposealternativewaysofsolvingdifferentialequations,theuse
of fixed points is proposed. A fixed point is that value, inside the
phasespaceinwhichthesystemvariableshavezerovariationinthe
absenceofexternaldisturbances(SoléandManrubia,2009).
Thatis,canberepresentedmathematically:
Ax = 0
In the case of R2 it is possible to determine the system behavior
when analyzes were separated from some fixed point. In the case of
asystemdefinedasfollowsaccordingto(Boccara,2010):
(cid:20) (cid:21)(cid:20) (cid:21)
dx β β x
= Ax = 11 12 1
dt β β x
21 22 2
WherethedeterminantofAisnonzero
det(A) = β β −β β (cid:54)= 0
11 22 12 21
Thefirstsolutionistheoriginthatestablishesatrivialresult,how-
everthesystemsolutionsdependontheeigenvaluesofA.
det(A−λI) = 0
ThetwoeigenvaluesprovidestheresultsforX,andinotherhand
Iistheidentitymatrix.
(cid:20) (cid:21)
1 0
I =
0 11.4. Modelsusedformeasuringmarketperformance 21
Inthisway,itcanobtain
(cid:20) (cid:21)
β −λ β
11 12 = (β −λ)(β −λ)−β β = 0
β β −λ 11 22 12 21
21 22
And hence it is possible to extract the quadratic equation (Boc-
cara,2010;SoléandManrubia,2009):
λ2 −λTrA+det(A) = 0
WhereTrAisthetraceofA,
TrA = β +β
11 22
So,thesolutionoftheeigenvaluesisdefinedasfollows(Soléand
Manrubia,2009):
(cid:112)
TrA± (TrA)2 −4det(A)
λ =
±
2
FinallytheeigenvectorsofthematrixAarethefollowing
Ax = λ x
± ± ±
For the case of R2 it will be two eigenvectors, each one corre-
sponding to the eigenvalues calculated with the above equation. In
this way the system supports an exact solution (Solé and Manrubia,
2009):
x = c eλ+tx +c eλ−tx
1 + 2 −
Wherein, the two constants c and c respond to the initial condi-
1 2
tionsofthesystem. Nowthetendencyofthesystemdependsonthe
signofthevalues(SoléandManrubia,2009):
• (λ ) < 0 Then at the point (0,0) the system is asymptotically
±
stable.
• Ifthereisaneigenvaluewithpositiverealpartthenx isunsta-
0
ble.
• (λ ) = 0 For both eigenvalues values if is zero for one and
±
negativefortheotherthenthepointx0isasymptoticallystable
butthatitisnotconvergent.
Theabovedescription(Boccara,2010)isintendedtoestablishthe
possible solutions to the equation describing the complex physical
phenomenon. After reaching this mathematical description, possi-
ble solutions can be as many as the phase space allows. Thus, for
the complexity, the solution of systems does not represent problems
besides stability of equilibrium. Sometimes from the technical point
of view is more complicated, the development of the equations that
describethebehaviorofthecomplexsystem.Chapter1. Electricitymarkets,gametheoryandcomplexity: State
22
oftheart
Chaos
Anegotiationprocesswheredifferentactorsareinvolved,whichseek
tomaximizetheirprofits(orparticularinterests),isanexampleofde-
terministic evolution when we have no more information than what
is intended to negotiate (Newman, 2003). Such interpretations for
many years were the center of the studies until the early twentieth
century when the study of phenomena, wanted to predict with cer-
taintytheevolutionwithmorevariablesintegrated(Levy,1994).
Poincaré(Boccara,2010)intheirpreviousstudies,establishedthat
thevariablesinvolvedinthedecisionprocess,coulddevelopachaotic
behaviorobservablethroughevolution. Thus,takesplacethebirthof
chaos as a differentiator for all the analysis that attempts to predict
with certainty the evolution of each system. Chaos does not mean
simplydisorder,chaosissimplyadifferentorder,whichmustbean-
alyzedinanotherway(Levy,1994).
Itispossibletoclassifythephenomenaaccordingtotheirlevelof
complexity and adding an additional element as the chaos (unpre-
dictable component), but does not mean that behaviors tend to be
random,chaosmeansthattheyhaveanunderlyingevolutionaryor-
der, always determinable, and when we know the initial conditions
(Levy,1994;SoléandManrubia,2009).
Then, by varying initial conditions, for real systems we can have
very significant effects, all of this in front to small changes, which
generatecascadeeffectorstrongimpactwithhighseverity(Kwapien´
andDroz˙dz˙,2012).
Anexampleofthiscanbethechangeintheregulationofelectric-
ity markets, specifically capital requirements, e.g. a company that
doesnothavethisrequirementcanpasstobeinsolventandgenerate
serious financial consequences. The chaos is deterministic because
there is some factor, or some component that determines their be-
havior(Levy,1994;Tesfatsion,2003).
Chaos theory has been misinterpreted because the first descrip-
tion is the existence of apparently disordered systems, but actually
what it claims chaos theory is finding the underlying order in data
apparentlyrandom(Levy,1994).
For purposes of this research, chaos represents a scenario, where
the electrical system exhibits difficulties from the financial point of
view, considering that one of agents doesn’t have the capacity to re-
spond to its commitments. That is, the generation of “default" situ-
ation (nonpayment) that implies the affectation of supply levels ac-
cordingtosmallchangesininitialconditions.
Andinitialconditionsarethestabilityatthebeginningofthepro-
cess, the organization of transfers and the accomplishment of the fi-
nancialconditionsforoperatethemarketasatrader.
The chaotic phenomena happen considering the first measure-
ment known as the autocorrelation C(τ) function is calculated from1.4. Modelsusedformeasuringmarketperformance 23
aseriesofdata(Levy,1994).
S = (x ,x ,...x ) with x∗ = fi− < x > in order to define the
1 2 n i µ
autocorrelationfunction(SoléandManrubia,2009).
N−1 N−1
(cid:88) (cid:88)
C(τ) = lim x∗ +τx∗ = lim < x − < x >>< x − < x >>
i i i+τ i
N→+∞ N→+∞
i=0 i=0
Inonedimensiontheapplicationofthefunctionstartsfromx =
i+1
f (x )toobtain(SoléandManrubia,2009):
µ i
N−1
(cid:88)
< x >= lim fi(x )
µ 0
N→+∞
i=0
Theimportanceofthisrepresentationisthatitallowsestablishing
a measure of irregularity of data with the aim of seeing whether or
notconvergentwithrespectofdeviationsfromtheaverage. Butifthe
series is periodic, at some points of the series, correlations will exist,
then it appearing maximum / minimum with the same statistical
value(SoléandManrubia,2009;Kwapien´ andDroz˙dz˙,2012).
Measure the autocorrelation of the data gives a clear signal on
the trend thereof and subsequent treatment (Kwapien´ and Droz˙dz˙,
2012). For the purposes of dynamic analysis, it is important to know
withsomecertaintythepossibilitiesofbehaviorinordertoestablish
actionplansandfuturestrategies.
However,theconnectionoftheanalysisofchaosandcomplexity,
allows the treatment of the systems and its understanding. In the
particular case of the electricity market, the ability to anticipate and
establish chain failures associated to an interruption in the power
supply can become a very powerful management tool when vari-
ablesareintegrated.
“IfabutterflystirsuptheairinBeijing,itcanchangethestormssystem
inNewYorknextmonth"(Gleick).
Selforganizedcriticality-SOC
These models were proposed by (Bak, Tang, and Wiesenfeld, 1988)
intryingtodescribemathematicallythebehaviorpatternofdifferent
systems with complex features or phenomena in nature (Bak, Tang,
and Wiesenfeld, 1988; Bak and Chen, 1991). The main condition is
thatsuchsystemscanevolvetocriticalstates,consideringthedistur-
bancegeneratedinternallywithoutdisturbingexternalagent.
Particularly the disturbance from the internal evolution of the
system is known as “avalanches", which are chained events affect-
ingsystemstabilityregardlessoftheperiodorscale(Jensen,1998).
Lots of physical phenomena have been studied from the SOC
modelssuchasearthquakes(SornetteandSornette,1989)wherestud-
ies developed by (Sornette and Sornette, 1989; Jensen, 1998) claimChapter1. Electricitymarkets,gametheoryandcomplexity: State
24
oftheart
that the cracks generated in the crust of the earth are spread in or-
dertowageastrongamountofenergy(SornetteandSornette,1989).
Eventhemechanicsoftherainssinceaccordingtostudiesconducted
by(Jensen,1998)theenergyprovidedslowlybythesuntoevaporate
thewater,isreleasedsuddenlyduringaneventofrain.
Thistypeofphenomenacanbeseenveryclearlyinthosesystems
that are in disequilibrium and passing have many degrees of free-
dom with an additional feature and are the nonlinearity (Bak and
Chen,1991).
One of the characteristics associated with the SOC models, is the
conditional similitude to chaotic systems, but so far the studies de-
veloped by physics that seek to prove the validity of the theories
do not have a final agreement on the necessary and sufficient con-
ditions for one system that presents a critical self-organized behav-
ior, according to studies conducted by (Sornette and Sornette, 1989;
Jensen,1998;BakandChen,1991)
1.4.4 Advantages
Many studies have focused on defining the energy demand levels
in the medium and long term over energy systems and their admin-
istration (Medina and Moreno, 2007; Sweeting, 2007; Weidlich and
Veit,2008),inordertoensurethesupplylevel. Theoptimizationpro-
cess meanwhile, reproduces such models to integrate the elements
and achieve high standards of performance at low costs. Growth is
evident,between1980and2005thelevelofdemandoffuelforpower
generation (in Mboe) grew nearly 60% (Sweeting, 2007), giving suf-
ficientbasesforstudyingthissubject.
Planning the performance of the energy system is not an easy
task, and therefore is necessary dispose of tools to achieve this goal,
starting from classical macroeconomic models unto the more inte-
gratedmodels.
The purpose of this work is to do planning of energy dispatched
butconsideringoptimalfinancialsystems,andtheresultsmusteval-
uatetheagentsintermsoffinancialrisk. Andthereareanadditional
goal related to the ability to predict the presence of negative events
associatedwiththeriskindicators.
Inturn,thecreationofusefultoolstoensurecommercialexchange
andtheenergysupply,itprovidesinnovativeelementsofanalysisin
businessdecisions. Similarlygeneratingfunctionalcomponentswho
seek the sustainability of stakeholders (central operators and trader
agents)fromthepointofviewofprofitabilityandsustainability.
This task requires of a series of conditions of economic nature,
technicalandofresourceavailability,beingsomeareassuchaspower
generation capacity, minimization of generation costs, minimization
the consumption of conventional resources and the equilibrium be-
tween supply and demand (Weidlich and Veit, 2008; Wolfram, 1999)1.4. Modelsusedformeasuringmarketperformance 25
thoserequiresspecialattentionbecausetheyimplicitlymustbeinte-
gratedintotheresults.
Historically there are some models that have been implemented
withquiteresultsinterestingfortheplanningoftheoperation,which
are responsible for identifying as the price or availability of energy
affects the general economy (Jackson, 2010; Krause et al., 2006; Wei-
dlich and Veit, 2008) with based on the impact on its gross domestic
product (GDP), unemployment, inflation, the producer price index,
exchangerate,amongothers,andviceversa.
Thegreatadvantageofthesehistoricalmodelsistheireaseofim-
plementation based on historical data and seasonality of the series.
Theproposalwiththisprojectistohaveatoolwithmorecomponent
thatcanbeintegratedwiththepreviousdevelopments.
However,aswasmentionedthroughoutthechapter,studieshave
focusedondeterminingoperationalandevengeneralexpositions,by
measuringtheeconomicimpactseverityofoperatingeventsinternal
orexternal.
Finally, the breakthrough that suggests this work, is the possibil-
ity of study directly the financial phenomenon implicit in the opera-
tions, and synchronize with operational and macroeconomic devel-
opments that results in more robust models for analysis, i.e. inte-
grated.
Thus, with a identification of interactions and impacts, we can
avoidaffectingthesystemsustainability,bymanaginganewbranch
of financial innovation, which is called systemic risk very different
fromconventionallyknownsystematicrisk.
Therefore we present the game theory, complexity, agent-based
modeling and other alternatives, such as better approaches to the
modeling of reality between agents in terms of financial risk. We do
not claim to measure profitability considering operations in the spot
market through hedging or optimizing portfolio of generation, but
bythewayofdoingtransactions.27
Chapter 2
Description: Situation of
Colombian electricity market
2.1 Colombian electricity market: review
The Colombian state, to the early 90’s made a detailed review of the
management and the energy sector achievements reached in several
years of operation. The results were very unfavorable because the
participants companies, they found many irregularities in terms of
operational, administrative and financial efficiency; even in the re-
sults highlight the declaration of insolvency of some of them. The
above process triggered the period of national rationing, and it was
forcedbetween1991-1992.
It was necessary to consider the modernization of the electricity
sector in Colombia. In this way, making adjustments in line with
the scheme implemented in the UK and other countries with similar
patterns of operation in energy markets, the country proceeded to
the restructuring. Similarly, the 1991 Constitution was signed in or-
der to ensure the provision of efficient public services over the head
of the state, in scenarios of competence and quality of the operation.
Thenitpresentedtheopportunitytointegratethesetwocurrentsde-
manding improved conditions of the energy market, i.e. quality and
competence.
The New Constitution designates the state’s obligation to pro-
vide the public services, allowing the main achievement regarding
the creation and definition of standards for the maintenance of the
entities responsible for the regulation, administration, planning and
control of the market. Private companies could provide public ser-
vices,butthestatewouldmakethetasksofregulationandcontrolof
theoperation(AguilarandDíaz,2004).
Article 365. Public services are inherent to the social purpose of the
State. The State should ensure its efficient delivery to all inhabitants of the
country(Colombia,1991).
Public services are subject to the legal regime established by law,
they may be provided by the State, directly or indirectly, by orga-
nized communities or individuals. In any case, the State shall main-
taintheregulation,controlandmonitoringoftheseservices(Aguilar
andDíaz,2004).28Chapter2. Description: SituationofColombianelectricitymarket
If for reasons of sovereignty or social interest, the State, by law
approved by a majority of the members of each chamber, initiated
by the Government decides to reserve certain strategic activities or
publicservicesmustcompensatepriorandfullytopeopleunderthat
law, deprived of the exercise of a lawful activity (Aguilar and Díaz,
2004).
By Decree 2119 of 1992, the former national commission of en-
ergy was transformed in "Unidad de planeación minero energética"
(UPME);hereformedtheMinistryofMinesandEnergy,andtheEn-
ergy Regulatory Commission, which is under the Ministry of mines
and Energy. The latter commission was created with the aim of ad-
vancingtheregulatoryactivitiesoftheenergysector,whichincludes
the price adjustments necessary for equitable service delivery, but
forgotthefinancialsustainability.
In 1994, the state promulgated the laws 142 (known as the Pub-
lic Services Law) and 143 (Electricity Act), for the design and subse-
quentconsolidationofaneffectiveinstitutionalstructure,whichsup-
ports the requirements of the utilities sector. Thus sought to achieve
goals in the face of social and economic sustainability, embodied in
the constitution (Aguilar and Díaz, 2004), and again the law men-
tionedthefinalitybutnottheassumptionsasacompetitivefinancial
structure.
Thenewregulatoryframework,createdthe“MercadodeEnergía
Mayorista" (MEM), which is monitored by the “Comisión de regu-
lación de Energía y Gas" (CREG). The objective of MEM was the or-
ganization of each of the participants about the transactions of buy-
ingandsellingenergy,providingastageoffreecompetition.
Another characteristic of MEM was the categorization of energy
contracts between generators and traders as financial assets, so that
it could establish the surpluses or shortages resulting from transac-
tions, also achieving the quantification of losses and profits versus
actualdemand,leavingtheinteractionsasaproblemofthemarket.
Some of the functions assigned to CREG, within the regulatory
framework are, establish the availability of conditions of an efficient
energy supply, define the rates and formulas related to regulated
users;determinethegradualliberalizationofthemarkettofreecom-
petition, approve charges for access and use of networks, establish-
ing the rules of operation of the national grid, the status of rationing
and the Code of networks (Sandoval et al., 2004). In no case the pro-
posalforensurethefinancialstabilitythroughthecreationofformu-
las.
Followingtheinstitutionalframework,managementofMEMwas
delegated to the “Administrador del Sistema de Intercambios Com-
erciales" (ASIC), which is responsible for making projections of con-
sumerdemandandsupplyofgenerators. Withthisinformation,itis
possibletomakeprogramingfortheidealdispatchandgettheprice
inthemarket,fromtheintersectionofsupplyanddemand.2.1. Colombianelectricitymarket: review 29
For its part the operation of the electricity market is made by the
“Centro Nacional de Despacho" (CND) whose function is to make
the dispatch of real energy from generating plants considering the
evolution of demand, the restrictions presented by the STN – “Sis-
tema de Transmisión Nacional", the ideal dispatch scheduling, and
controlrequirementsoftheenergyfrequency.
By comparison, the delegated authority to develop projects asso-
ciated with the expansion plans of the energy market, which are in
line with national development plans, is the “Unidad de Planeación
Minero Energética" (UPME). And is responsible also recording the
generation and transmission projects, they evaluate the concepts on
thetechnicalandfinancialfeasibility,thefuturesplansforconnection
to the STN and actively participate in decisions led by the ministry
of mines and energy in the face to the fulfillment of constitutional
order.
The“SuperintendenciadeServiciosPúblicosDomiciliarios"(SSPD)
iis the guarantor, providing monitoring and supervising of the par-
ticipants in the energy market. This entity has the power to inter-
vene and punish companies that repeatedly violate the established
standards (Sandoval et al., 2004). Particularly the monitoring of fi-
nancialandoperationalresultsofthecompaniesundersurveillance,
arecatalystswhencontinuityiscommittedtotheprovisionofpublic
services, which boosts the action of the SSPD. But continuing with
the analysis, there is no entity responsible of the financial relation-
shipbetweenagents.
The state with the aim of providing transparency to the electric-
ity market, and through the regulatory framework has achieved the
separationofthecharacteristicsofeachservicewithintheMEMeco-
nomicactivities. Thefigure2.1proposesageneralschemeoftheelec-
tricity market, and it represents the relationships between the vari-
ousagentsandentitiesinvolved.
Where,
• ASIC:AdministradordelSistemadeIntercambiosComerciales.
• CND:CentroNacionaldeDespacho.
• CNO:CentroNacionaldeOperación.
• CAC:ComitéAsesordeComercialización.
• CAPT:LiquidadoryAdministradordeCuentasdelSTN.
• LAC:AdministradordelSistemadeIntercambiosComerciales.
• MEM:MercadodeEnergíaMayorista.
Since the enactment of laws 142 and 143 of 1994, Colombia has
advancedtoaprocessthataimstoachieveefficiencyintheprovision30Chapter2. Description: SituationofColombianelectricitymarket
FIGURE 2.1: Operational structure for electricity mar-
ket
Source:ComisióndeRegulacióndeEnergíayGas(CREG)
of services derived energy demand in terms of quality and competi-
tiveness (Aguilar and Díaz, 2004; Sandoval et al., 2004). This allows
thepresenceoftheliberalizationofthemarketbetweenagentsgener-
ators and traders with the aim of ensuring transparency in price for-
mation,whilethetransmissionisconstitutedasaregulatedmonopoly
thatlaterbecameinanoligopoly.
The creation of MEM “Mercado de Energía Mayorista", the sub-
sequent establishment of the Colombian Energy Exchange in 1995
(Aguilar and Díaz, 2004), creating “Derivex" (for derivatives trad-
ing) and establishment of the Central Chamber of counterparty risk
for compliance with leveraged transactions, seek the proper func-
tioning of the energy market, where all participants act on an equal
footingandunderstrictqualitystandardsallowingfreecompetition.
The basis for market functioning and creation of Colombian En-
ergy Exchange, where the State established the right conditions for
the generation and procurement guidelines for energy on spot mar-
kets,forwardmarketsandcontracts,beganitstermin1995,through
theresolutionsCREG24of1995and25of1995. Henceforthallregu-
latorychangeshavebeenreferredtotheseresolutionssothatthereg-
ulation of the operation of the system have been based on the same
fundamentals. Nevertheless all the components of the framework
donotconsidertheproblemsderivativeofdishonoringthebusiness
commitmentsacquiredbetweenagents.
In other words, the regulation law defines the need for interven-
tion in energy prices even in reservoirs when water levels are lower
to higher operating minimal (decrease in supply). In this aspect, the
charge for capacity was created because of the consideration to the
guarantee of generation capacity (supply securing), among others,2.1. Colombianelectricitymarket: review 31
butagainitrefersfromoperationalperspective,becausetheweather
and rains are variables with high impact and difficult to predict, in-
stead financial conditions can change in specific times according to
thelaw,butitisnotnecessarilytrue.
Then,theclassificationbetweencogeneration,lowgeneratorsand
self-generatorswastheanswertothespecializationofthesystemin
the main activity (generation), establishing limits required for bids
on the stock market as long as its generating capacity was superior
to20MWandensuringthatmarketmakingisrecurrentwithoutdis-
continuity in the prices formation, it means more operative controls
andtheabsenceofcorporatecontrols.
Themarketorganization,asmentionedaboveisdesignedinfour
main activities: the generation that is the production of electricalen-
ergy, activity that must be connected to STN; the second one is the
transmission which is responsible for transporting energy through
its own infrastructure (at or above 220 KV lines), third the distribu-
tionwithsimilaractivitiesonlyonalowervoltage(lessthan220KV)
and finally trading, specifically geared to the purchase and sale of
electricity.
In the trading activity, transactions may be through bilateral fi-
nancialcontracts,freelyagreebetweentheparties,orthrough“Colom-
bianEnergyExchange"transactionssimilartothestockmarketwhere
the price adjustment responds to movements between supply and
demand.
According to UPME, considering the historical development of
the energy sector and in attention of all its elements, it is possible to
classify the events occurred with direct impact on the operation in
three major components, which demanded a revision of the regula-
tionandspecializetheoperation. Thecomponentsareasfollow:
1. Institutionalevents: fromthepromulgationoftheconstitution
in1991,whendesignatingthestate’sobligationtoprovidepub-
lic services. Major milestone, concerning to the creation and
definitionofstandardsformarketoperation.
2. Regulatoryevents: wheretheactivitiesassociatedwiththegen-
eration, transmission and trading were regulated. Guidelines
forenergycontractswerecreatedthroughbilateralagreements
and resolutions CREG 24, 1995, the Commercial Code, the res-
olutionCREG25of1995andthenetworkcodestartingtheop-
erationoftheenergystockexchange.
3. External events: because the inclusion of factors that have had
animpactofexternalorigin,allowedthedetailedreviewofop-
eratingconditionswiththeobjectiveofspecializingthemarket
performance. Thus, are highlighted the “fenómeno del niño"
occurredbetween1997and1998,armedconflictwhichinvolved
damages in the national grid and the economic recession that
tookplacebetween1998and2000.32Chapter2. Description: SituationofColombianelectricitymarket
Theorganizationofthemarketisolatedofactivitiesthattakeplace
insideofhimandthecompositionoftheentitiesthatmanageandop-
eratethesystem,isbasedonagents,generators,transporters,traders,
distributors and consumers. Which leads to the interaction between
themandcreatecertainlevelsofcomplexity.
Thispeculiarityhasnotbeenanalyzedbecauseofthemodelsim-
plementedsofar,areconcentratedintheestimationofenergyprices,
the modeling of demand levels, predicting own agents strategies,
identification the best practice of energy policies, simulating supply
failures, blackouts, among others (Borenstein, Bushnell, and Knittel,
1999; Medina and Moreno, 2007; Stoft, 2002; Sweeting, 2007; Wei-
dlichand Veit, 2008; Wiszniewska-Matyszkiel et al.,2008). Thisdoes
not incorporate the peculiarities of the system around the financial
interactionofagents,andthepossibilityoffailurebecauseacovenant
isnoreached,forexample.
Forinstance,somegeneratorsconsiderthatthevolumesoftrans-
actions in energy exchange, the ideal dispatch, historical bilateral
contracts, inflexibility, or even changes in regulation are decisive for
the formation of prices in spot markets. But, usually they don’t con-
template rigorously the possibility that an agent present liquidity
problems with high probability of counterparty risks, which affects
thedevelopmentofthespotpriceandmarketstability.
It is important to note that energy demand must be satisfied un-
der the conditions of the system, that’s why the concentration of re-
searcheffortswillbedirectedatensuringthefunctioningofthemar-
ket, allowing anticipate materialization of financial risk, and proper
featuresofmarketfunctioning.
In the figure 2.2 we present the main components of the energy
market considering state intervention, in turn some of its own mar-
ketinteractionsbetweenagentsandthemanagementandcontrolen-
tities are presented. At each level it becomes possible to identify the
participants, being the CREG the agency responsible for the regula-
tion and UPME responsible for planning. There is an entity desig-
natedfortheoperationofthesystem,anditisresponsibleforensur-
ing the operation and functionality of the market (Aguilar and Díaz,
2004)hisnameisXM“ExpertosenMercados".
And thanks to the figure 2.2 is it possible to identify that XM is
the company responsible of the fulfillment of financial transactions,
but is complicated take control of all financial decision inside of the
agents.
2.2 Operation of the electricity market
The electricity market consists of 5 major participants: generators,
transmitters,distributors,tradersandconsumers,whicharedescribed
below(AguilarandDíaz,2004):2.2. Operationoftheelectricitymarket 33
FIGURE 2.2: Compositionoftheelectricitymarket
Source:Unidaddeplaneaciónmineroenergética(UPME)
2.2.1 Generators
The generators are companies that produce energy, which can be
traded on the Colombian Energy Exchange or through bilateral con-
tracts. Installed capacity greater than or equal to 20 MW and differ-
entgenerationofedgeofwater(hydro)mustsubmitoffersofenergy
daily, valued at the price that forms per kilowatt / hour, in parallel
must declare the availability of generation in order to program the
dispatches.
2.2.2 Transmitters
Thesecompaniesrecordtheirincomethroughremunerationindexed
to some economic index, and the remuneration doesn’t depend of
the used of the infrastructure (continuous flow of energy, conges-
tion, etc.). This remuneration is done by calculating a new replace-
ment value of network assets (present value discounted at a capital
cost) and evolves depending on PPI (producer price index) nominal
forthepreviousfiscalyear. Simplytheincomeisfixedandacknowl-
edgedfromtheavailabilityoftransmissionassetsandthepossibility
oftheiruse.
2.2.3 Distributors
Thesearecompanieswhosebusinessisalsoconcentratedinthetrans-
portation of energy, but in voltage levels below 220 KW, allowing34Chapter2. Description: SituationofColombianelectricitymarket
them to attend other lower voltage systems. These systems are di-
vided into two: “sistemas de transmisión regional" (STR) and “sis-
temas de distribución local" (SDL), and distributors are responsible
forprovidingservicestooneormoretradingmarkets.
2.2.4 Traders
Areagentsintermediarieswhomakeanintermediationbusiness,in-
teracting with claimants of energy, generators, transmitters and dis-
tributors. Theycanoperateinresponsetotheregulatedmarket(con-
sumption of less than 0.1 MW), not regulated or even both. It is a
treasury management business whose operation is similar to an in-
vestment fund, because they are buying and selling energy from the
positionarbitrageur,howevertheydon’tspeculatewiththepricebe-
cause it can lead to sanctions by the regulator. Risk exposures con-
centrated issues like financial affairs, credit, liquidity evaluations,
market and operational situations, and all conditions must be given
forcarriedoutthedispatchofenergy.
2.2.5 Consumers
Inthesamewaythatthematerialsproducers(asairon,steel,cooper,
coal), all consumers are closing the cycle thanks to its demand po-
sition of the energy produced. They are legal entities or individuals
who require this product to ensure operation or just for everyday
activities, thus the consumer determines the fluctuations in supply
accordingtothebehavioroftheeconomy.
The operator of the energy market in Colombia has under its ad-
ministrationthefunctionsof“CentroNacionaldeDespacho”(CND),
to manage the “Sistema de Intercambios Comerciales" (ASIC) aand
finally establish and manage accounts usage of charges in national
networks (ASIC). The representation can be seen in figure 2.3. Sim-
ilarly, the planning of the operation and the direct relationship with
the agents, are crucial for the fulfillment of transactions. The opera-
tor evaluates the minimum levels of liquidity, solvency, capital and
other financial conditions, for agents in order to participate in the
operationinanequitablemannerwithoutcompromisingthesupply,
butthesituationintheaccountsofagentsisoutofcontrolbecauseof
thatthecompleteinformationispublishedeach3months.
One of the necessary conditions for ensuring energy supplies,
wants to avoid the concentration of activities in the energy market,
namely the generation, transmission, distribution and trading. Re-
garding generation (installed capacity), no company can own more
than 25% of total available generation in the country, which ensures
the energy production function as a diversified portfolio despite the
fact of large hydro exhibition that has Colombia. Likewise, a similar2.2. Operationoftheelectricitymarket 35
FIGURE 2.3: Functionsoftheelectricitymarketopera-
tor
Source:XM
percentage for the trading and distribution activities (no more than
25%) and the percentage extend through figures like equity method
andindirectownership(businesscastling)(Sandovaletal.,2004).
Thecalculationofcommercialoffersisperformedfromthemethod-
ology of asset allocation using a tool for financial market manage-
ment (Kuznetsova, 2014). All participants must provide financial
guaranteesasrequiredbytheregulationandinthecaseofgenerators
andtraders,existsadirectrequesttoparticipateinenergyexchange.
Thus, each participant agent has a number of rights and obligations
to be met fully, with the final purpose of ensured the power supply
andavoidingrisksthatcouldposeahighseverity.
Aspecificcasethatconcernstotheplanningcentralofenergyhas
to do with the re-dispatch, which refers to the rescheduling of initial
supply. If there are operational deviations around 5% (VaR at 95%
of confidence) on the generation of programmed energy, will lead to
penalties for generators that will be paid in cash and the settlement
is established considering the spot energy price and the price of of-
fer that the generator present when they make the reprogramming
(Sandovaletal.,2004).
This is a sample of intervention by the operator, and in the case
of financial exposure, nowadays the legislation considers the capital
capacitybutnotthematerializationofsystemicriskgeneratedbythe
interactions.
The above is a specific case of risks, and necessarily will be con-
sidered when all exposures of the agents should be integrated, also
wheninvestigationsidentifiedwhatarethebestwaystorelationthe
variablesinaglobalcontextofrisks. Inanycase,therepresentations
of integral physical phenomena but in this project the consideration36Chapter2. Description: SituationofColombianelectricitymarket
offinancialbranch.
2.3 Normativity
During2015theregulatoryactivityoftheelectricitysectorwasmainly
focused on the adoption of measures in the Wholesale Energy Mar-
ketduringthepresenceof“ElNiño",thedefinitionandmodification
of the rules for participation in the market for auto-generators, co-
generatorsandsmallplants.
The regulated market is directly hired and operated by distri-
bution companies, spanning industrial, commercial and residential
users with lower energy demands to 55 MW/h. In this market, the
tariff structure is established by the regulatory agency CREG based
on levels of demand and economic conditions. It is this market are
concentrated almost all users in the country. The regulator for col-
lect and calculate the tariff, approves the formula, and any user is
attendedregardlessofconsumption.
On the other hand in the unregulated market, the industry par-
ticipates and all users who have a high-energy consumption. Cur-
rently an unregulated user is a consumer who needs energy, greater
or equal than 55 MWh / month. Unlike user regulated, the trading
priceandgenerationisfreelyagreedthroughaprocessofnegotiation
betweentheconsumerandtheseller.
2.4 Hiring energy
Tradersbuyenergyfromgenerationcompaniesthroughbilateralcon-
tracts to two or three years (which allows them to negotiate in ad-
vance the price and know in advance the costs), or by purchase on
thestockexchangeofenergy,whichitissometimesnecessarybutex-
posed to market fluctuations. This is the reason why, the Colombian
market works as a complex system because as to execute the trans-
action on the market, the agent must evaluate a number of variables
inordertocompletetheorder.
Most traders of the country choose the first scheme, the long-
termcontracts,oramixedformulathatcombinesbothmethods. The
power purchase long-term contracts represents approximately 85%
ofthecountry’sdemand. Inthatsense,itisinterestingformulatethe
market because the operation can be anticipated from the complex
dynamicsperspectiveandallowsmanagingfinancialrisk.
Long-termcontractscommitgeneratorstoreachthesupplyacer-
tain amount of energy at an agreed price, which lowers the price
volatility of electricity delivered to the end user. Generators back
thiscontractedenergy. Theymustsecuretheenergyofferedandthey
mustdothroughitsowngeneration,andthatiftheproductionisnot2.5. RiskFactorsintheColombianMarket 37
enough, they should enter into contracts with other agents, or buy it
inthespotmarket.
The quantity of energy supply that generators sell into the spot
market corresponds to the expected water inflows in the future and
totheavailabilityofnaturalgasandotherfuels. Forthisreason,they
sell energy contracts above its generation capacity, which represents
ariskforthegenerator.
Traderscangotothespotmarketandpurchaseelectricityatmar-
ketpricesthatreflectthedifferentialbetweensupplyanddemandof
energy at the time of the energy transaction. Go to the spot market
involves risk for traders, as prices have high volatilities, which they
transferredtousersbytariffs.
Buy on the spot market is an option and not an obligation, and
therefore at any time this can be interpreted as a restriction strategy
inducedinordertospeculatewithprices.
The Colombian electricity system is characterized by high price
volatilityinthespotmarket,largelyduetodown-regulationofreser-
voirs,andsomeonewhowantstobuyenergyintheenergystockex-
change, but without price hedges, is taking the same risk as assume
ageneratorwhenitsoldaboveitsgenerationcapacity.
Finally, to participate in the market as an agent, there are a num-
berofoperationalrequirementsandfinancial,suchasatechnicaleq-
uity that support the buying and selling energy depending on the
sizeofthecompanyandthecommercialambitions. Theymustdemon-
strateitsfinancialcapacity tocarryouttransactionsinthe wholesale
energymarket.
Monthlypowerpurchasetransactionsofeverytraderwillbecon-
ditioned to the evolution of technical equity indicator, which will be
establishedbytheCREGinaseparateresolution.
2.5 Risk Factors in the Colombian Market
The number of active agents in the Colombian market is approxi-
mately 152 including generators (44), transmitters (10), traders (69)
and distributors (29). Nevertheless approximately 63% of market
transactions are explained and executed by six agents considered as
the most representative. For this reason the results in the chapter 5,
consider the representation of a micro electricity market with those
participants(6total)forwhichfinancialinformationisavailablecon-
solidatedwithyear-end2015. Theabovestatementconfirmsthecon-
centrationofriskin6agents.
When considering the levels of impact of each risk factor on the
agents involved in the Colombian electricity market (weather, eco-
nomicconditions,armedconflict,operationalfailures,demand,etc.),
it is necessary to define critical scales of affectation, which include38Chapter2. Description: SituationofColombianelectricitymarket
the probability that a risk event occurs with their respective finan-
cial severity. This will allow the construction of a comprehensive
riskmapledtoeconomicquantificationofunmetdemandalongside
elementsofafinancialnaturethatmayarise.
The classifications of risk factors for certain agents establish the
first approach with the aim of obtaining a comprehensive map, for
example the reduction of water reserves in the country, affect the
availability of generation, leading to an increase in the market vul-
nerabilitysincethereisadirectimpactonsupplylevels. Theinternal
armed conflict has great importance for the overall levels of risk ex-
posure, in view of the damage to the electrical infrastructure of the
country;theyimpacttheavailabilityofsupplyandthuslimitthevol-
umeofspotandforwardtransactions.
Similarly,internationalmacroeconomicconditionsdisturbtheevo-
lution of the local electricity market, either by the contraction of do-
mestic demand levels that would directly affect GDP, or by the side
ofthesupplyofgoodsasexportsalsocandecline,compromisingthe
competitivepositionofthecountry. Theoilandminingthataregreat
electricityplaintiffsbecomecatalyststomeasuretheevolutionofthe
energy market, requiring permanent monitoring of the contexts of
thesesectors.
The electricity market, in addition to the risks mentioned above,
facessomethatareinherentinitsoperation(markettopology)within
which stand the risk of blackout, by network failures, risk of human
errorsandoperationtechnologicalassets,defaultsonbilateraltrans-
actionsorcontractsinspotmarkets,amongothers.
Likewise,financialandeconomicindicatorsofeachagentarefun-
damentaltothetradingofenergycontracts. Inotherwordsfortraders,
generators,transmittersanddistributorsisimportanttopresentgood
results in its financial statements, in order to mitigate risk factors
such as solvency, liquidity, responsiveness, interest coverage, debt
service, financial leverage and operating leverage among others, en-
ablingthemtoactivelyparticipateinthebuyingandsellingenergy.
In short, the comprehensive management of financial and corpo-
rateriskencouragestheagentstocreateactivemanagementschemes,
sincetheresponsibilitytokeepthemarketoperating,largelybelongs
tothem.
Withtheaimofaddressingtheprojectasamodelofvulnerability
oftheColombianelectricalsystem,wehavedevelopedmethodolog-
ical approaches through systemic approaches for which the charac-
terization, simulation and modeling of subsystems. All of the ap-
proaches consider the interrelationships and interdependencies of
the components of the process from a risks method with the respec-
tiveeconomicquantification,whichseekstoidentifypotentiallosses
and the establishment of more rigorous management about risk fac-
tors.2.5. RiskFactorsintheColombianMarket 39
FIGURE 2.4: Processofthemodeling,financialvulner-
abilityoftheelectricitymarket
Source:Computationsbyauthor
Figure 2.4 proposes a planning of all the elements of the Colom-
bian electricity market, reviewing the states associated with the con-
structionoftheriskmodel. Inputscontemplatethemarketstructure,
agents, energy prices, changes in demand and supply among oth-
ers. Whilethemodelisresponsibleforlinkingtheelementstofinally
establishriskindicatorsthatquantifymarketvulnerability.
The government has the task of planning the operation through
entitiesdesignatedforthatpurpose. Theymakeelectricalanalysison
what they hope will be the behavior of the system and they present
the information of the main variables to maintain quality, reliability
and safety in the attending of demand under the current regulatory
framework.
Theoperationiscoordinated,monitoredandtheoperationiscon-
trolled in order to find the optimal utilization of resources for the
provision of electric service, through continuous monitoring of hy-
dro and thermal units and network interconnection. The necessary
actions to maintain the levels of voltage and frequency within the
ranges established qualities in the current regulatory framework are40Chapter2. Description: SituationofColombianelectricitymarket
coordinated.
2.6 Space research in electricity markets
The market organization and composition of the entities responsible
for its administration and operation, is based on agents, which are,
generators, transporters, traders, distributors and consumers. This
entails that the interaction between them have certain levels of com-
plexity, even more when they exchanges cash flows between them.
This specific financial complexity, has not been tested in studies de-
veloped by (Borenstein, Bushnell, and Knittel, 1999; Medina and
Moreno, 2007; Stoft, 2002; Sweeting, 2007; Weidlich and Veit, 2008;
Wiszniewska-Matyszkiel et al., 2008), given that the models imple-
mented so far are concentrated in the estimation of energy prices,
themodelingofdemandlevels,thepredictionofstrategiesfollowed
bygeneratoragents,identifyingbestpracticesinenergypolicies,the
simulation of supply failures, and even the severity of operational
risks.
This does not incorporate the peculiarities of system around the
financial and economic interaction of the agents in charge of buying
and selling energy to ensure the supply, which is why this research
projectisrelevantandpertinent.
In other words, in many investigations aimed at electricity mar-
kets (Gnansounou et al., 2004; Stoft, 2002) the results do not con-
sider the possibility that a trader or generator presented problems
of liquidity or solvency with highly likely to materialize their coun-
terparty risks, which affects the creation of the price and the market
stabilitybecausethesupplyiscompromised.
At the same time, energy demand should be reached despite the
conditionsofthesystem,forthisreasontheconcentrationofresearch
efforts will be directed at ensuring the functioning of the market
fromallperspectives,allowinganticipatethematerializationofoper-
ationalrisk,strategicrisk,legalrisk,marketrisk,technologicalexpo-
sition, financial risk, and the proper system operation. Finally con-
sideringthisresearchproject,theinclusionoffinancialcomponent.
In that sense, the advances in (Apt et al., 2004; Sweeting, 2007;
Young, Poletti, and Browne, 2014) have helped to achieve results of
operational, strategic, technological type and even in markets func-
tionality, however there is an analytical gap in studies when the fi-
nancial component is an assumption that input always true, and is
fulfilled in all cases. The problem is because one of the assump-
tions for finding results is the economic and financial feasibility of
the agents and as is well known, the financial component depends
on a lot of difficult elements to integrate and not always is satisfied
intherealoperation.41
Chapter 3
Key Risk Indicators: KRI
3.1 General overview
The indicators generally are classified into three major classes: as
measuresofrisk(KRI)andperformancemeasures(“Keyperformance
indicators" or KPI) and finally as control measures (“Key indicator
control" or KCI) (Krause and Arora, 2010; Scandizzo, 2005). The
latter serve to measure the effectiveness of specific controls in the
process, indicating increased some chance or residual impact (Scan-
dizzo, 2005; Beasley, Branson, and Hancock, 2010; Lam et al., 2006)
while the KPI can determine how strategic performance of any or-
ganization evolves, it means they are measures for later stages and
thosemeasuresarelackingofanticipation.
Meanwhile, the development of metrics for determining the oc-
currence of an event with a probability level is in synthesis the cre-
ation of a KRI (Lam et al., 2006). That said, it is important to add in
theprocessofconstructionoftheKRI,thelevelofrisktoleranceafter
a study of aversion, because an intolerable event can translate high
businesslossesthatkeepfarawaythecompaniesincompliancewith
the objectives. In turn, the application of indicators depends largely
onthesectorinwhichbusinessesoperate.
WithintheconstructionoftheKRI,havebeenconsideredmetrics
that for their characteristics can be classified as KPI, mainly those
of financial nature such as debt, return on equity, coverage, among
others. However, these results are not evaluated in isolation way,
i.e., limits or thresholds that indicators should respect are proposed,
instead of viewing them as a measure of performance. This allows
management to have tools since the establishment of ranges for the
behavior of KRI, which without the existence of these ranges, they
wouldbeclassifiedasKPI.
Thewholesaletradeforexamplecanhavespecificindicatorssuch
as the number of product losses for each type of goods sold so that
the analyzes provides in specific periods of time, the following re-
sults: what are the products that generate value, which ones destroy
value, which it is the evolution in certain period, in order to find
thosemostcriticalproducts.42 Chapter3. KeyRiskIndicators: KRI
But the challenge facing every organization lies not only in the
identification and implementation of KRI in the business environ-
ment, but also in the way that the company communicate to stake-
holders, the level of importance and metrics implemented, because
sometimes are confusing (Parmenter, 2015). In this sense budgets
play an important role since they start from setting goals at the be-
ginningofeachperiodandthusriskindicatorsshouldbefocusedon
meetingtheseobjectives.
TheaccuracyoftheKRIshouldreflecteachnegativeimpact,which
corresponds on the figures of the companies, for this reason it is
sometimes possible to confuse the key risk indicators KRI with per-
formance indicators or KPI’s. As example profitability indicators in
an organization, such as returns of capital, return on assets or in-
ternal rates of return, are used to evaluate the performance of the
organizationbutundernocircumstancesareclassifiedascriticalrisk
factors.
For this reason, often the KRI indicators are pigeonholed in mea-
suring operational risk, given that usually are parameters such as
the number of failed operations, rotations inventory or personnel,
number of failures in systems, frequencies, omissions, among others
(Scandizzo,2005). Inturn,theymaybequalitativeorquantitativeal-
though sometimes they lose objectivity because the metrics used are
ambiguousorwithouttherespectiveassumptionsforprovetheirve-
racity.
However, for purposes of this research project, the proposed ap-
plication of the KRI falls squarely on the strategic objectives of the
organizations generating an indirect link with KPI. Thus the results
suggest an improvement in the way to measure the achievement of
objectivesthroughdirectmonitoringofKRI,allowingthepossibility
of exercises of comparison with the results of the indicators derived
fromotherorganizations.
Thechapterisorganizedasfollows;firstthebasicdefinitionsthat
generatedisturbancesandtheconsequentcreationofkeyriskindica-
tors are presented. Following is a brief description of the Enterprise
Risk Management as an administrative tool. Third, the adequacy of
ranges used for the analysis and interpretation of results. Posteri-
orly indicators applied in the electricity markets are detailed and a
proposal for those that best fit the analysis in question, with a rat-
ing between macro and micro indicators derived from this research
andconsideringresultsfrom(Sioshansi,2002)andfinallyaspacefor
futurediscussionsisporposed.
3.2 Risk analysis
Theriskmeasurementisanexerciseinlifelonglearningcorrespond-
ingtoallmembersinvolvedintheorganization,giventhattoensure3.2. Riskanalysis 43
sustainability is necessary to keep under control most variables that
threatenbusinessviability(Kaplan,1997).
Thisexerciseconsistsof threeelementsthatworkon ascheduled
basis and are as follows: First, the classification of risk given the im-
pacttheyhavewithrespecttothelimitationinthescopeofcorporate
objectives. Second one, the approximation to a measure of the likely
impact on the results, if the materialization of risk occurs, in other
words, evaluation. And finally, thirdly management and risk con-
trol, through the establishment of KRI, which are defined as tools
to manage risk into an acceptable level for the strategy (Hertz and
Thomas,1983).
Meanwhile,monitoringisveryimportantbecauseitispossibleto
predict with some certainty some adverse impact on business strat-
egy, which is associated accurately the perception of risk thrown by
thoseKRI(HertzandThomas,1983;Lametal.,2006). Thusagilityin
the reaction in front of risks is acquired, following the cycle consist-
ingofthethreestepsmentionedabove,classification,evaluationand
management (control), enabling a good routing around risk (Hertz
and Thomas, 1983). The monitoring, becomes in an integral pro-
cess for strategic risk management (Hertz and Thomas, 1983; Jorion,
1996) and seeks with no doubt, remain aligned with the objectives
of the organization. Therefore the generation of information about
previous results and subsequent studies creates elements that allow
understandingtheevolutionofrisksandtheenvironment.
Inthiscontext,companiesfaceanumberofdisruptorsordisturb-
ingelementsthatcancausethegenerationofmanyriskswithstrate-
gic impact and these in turn go unnoticed due to the large volume,
allowing in many cases not be studied in depth (Jorion, 1996). From
the KRI, risk analysts can manage more concretely the existence of
disruptorsordisturbingelements,steppingaheadintheanticipation
ofcontingenciescausedbyriskevents.
A disturbing element or disruptor is a source of risk, i.e. a cat-
alyst or risk generator, which comes from a weakness from the en-
vironment, or even from a fortress of the same environment (Renn
and Klinke, 2004). This current, drives or transformed sectors, and
given its nature can be beneficial or detrimental to ensure the op-
erations. That generates scenarios for value creation or destruction
from a corporate point of view, and in turn becomes an element for
anydecision.
Disruptors can be classified into the following groups according
to their level of impact on the strategic objectives of the companies
giventheirnatureandhowtheyfitbusinessareas:
1. Technology disruptors: Associated with the need for techno-
logicalprogresstokeepattheforefrontorganizations.44 Chapter3. KeyRiskIndicators: KRI
2. Operational disruptors: Related with the generation of inade-
quacies in the processes, internal systems and external events
thatarenotanticipated.
3. Demographic Disruptor: Responding to gender preferences
andpopulations,adjustedtoconsumerhabits.
4. Regulatorydisruptors: Linkedtochangesthatexertcontrolen-
titiesfortheproperfunctioningofmarkets.
5. EconomicorfinancialDisruptors: Presentindecisionsinvolv-
ing normal functioning of organizations in crisis scenarios or
expansion.
6. Political Disruptors: Concerning the physical locations where
business activity are made and its relevance to the situation of
developingcountriesorregions.
However,understandingtheoperationofthedisruptorandrank-
ingassourcesofrisk,itispossibletoestablishafirstdefinitionofthe
KRI. The key risk indicators are measures developed to manage ap-
petiteandtolerancethatisimplicitinthedailyoperationsregarding
therisks(Lametal.,2006).Theappetiteforitspart,isthelevelofrisk
that an organization is willing to accept in the process of achieving
objectives, while tolerance is the variation from this level, in relation
to the approval of organizational goals. KRI can be ratios, volumes,
amounts,percentages,days,months,monetaryvalues,distances,ca-
pacities, rates and generally any measure adapted to the specific sit-
uationthatisunderanalysis.
A further step is the realization of monitoring risks, where it is
common to use stoplights or states of situation on the KRI (Kaplan,
1997), which can establish early warning and sometimes anticipate
thematerializationofsevereeventsforbusinessresults. Thuswithin
the control panels it’s necessary to present current situations, trends
and future outlook using visual media such as the use of colors in
thestatesofsituations.
To understand the use of the states of situation using the follow-
ing example is intended to illustrate in greater detail: Basel in its
presentation requirements for the management of financial institu-
tions, proposes a liquidity indicator is calculated by the following
equiation(RepulloandSaurinaSalas,2011):
LiquidAssets
FinancialLiquidity = ≥ 100% (3.1)
netcashoutflows
The results show a percentage that refers to the amount of avail-
ability of cash owned by the company, to meet commitments and
disbursementsforthenext30days(RepulloandSaurinaSalas,2011).
Basel III in their definitions proposed that the indicator exceeds
100% given that the level of obligations of financial institutions is3.2. Riskanalysis 45
high (Committee et al., 2010). Whereby, the regulation seeks to en-
surecomplianceofoperationsinordertoensuresustainabilityinthe
system.
Now, if the indicator is below 100% according to the regulations
of Basel the company will incur a liquidity risk which is defined as
the inability to honor its commitments in the short term (Commit-
tee et al., 2010), understanding these commitments as the material-
ization its risks. Similarly liquid assets are classified at level 1 and
level 2, level 2 being those that can be sold on the market at prices
lower than those recorded in book value (Committee et al., 2010).
This latter feature requires that in stress scenarios the company be
seenintheobligationtoprovideimmediateresourcestohonorcom-
mitments despite the existence of assets Level 2 reaffirming a lower
limitof100%.
That Said that it is evident the liquidity indicator for Financial
Institutions Should be classified as KRI, it is possible That Given to
monitor the risk of the company through ITS calculation. Similarly
disruptive causing the risk (or source thereof) will be one of an eco-
nomicnaturebecauseitdirectlyaffectsthesustainabilityofthecom-
panyintermsofprofitability.
For analysis and in line with the use of control charts, it’s nec-
essary to have a current situation from the latest financial figures
reported, a trend about where the indicator can go in the coming
periods,andthenanestimateorperspectivetoithasprojected. That
said,eachfinancialcompanyforgetinternalresultsandtheexternal
analysts for independent manner, define a range over which can be
inacritical,sustainableorappropriatemeasure,whichwillbecalled
"riskstoplights"fromtheuseofcolors.
• Red: criticalmeasureofliquidity.
• Yellow: Measuresustainableliquidity.
• Green: adequatemeasureofliquidity.
Thefigure3.1offersavisualschemeformanagingoftheliquidity
indicator that responds to the state situation (that place where he is)
with the aim of taking corrective measures required. In the example
you can see that the indicator is currently 105% but the trend is to
decrease to 101% and he approaches to the minimum required level
demandedbyregulation.
Anstudyin2009foundthat40%offinancialservicescompanies,
were in the process of adopting and developing KRI (Beasley, Bran-
son, and Hancock, 2010), however there is little information about
what kind of KRI should be implemented and the effectiveness in
operationalrisk(Beasley,Branson,andHancock,2010). Whatisclear
is the usefulness of such indicators in later stage the financial crisis
unleashedin2008whenriskmeasureswerequitepermissive.46 Chapter3. KeyRiskIndicators: KRI
FIGURE 3.1: Exampleconsideringliquidity
Source:Computationsbyauthor-BaselIII
3.3 Enterprise Risk Management −ERM−
Afterthedescriptionofthestagesrequiredintheriskanalysisinthe
previous paragraph, it is possible to integrate all the elements from
theenterpriseriskmanagement,whichbecomesatoolformanaging
organizations. Enterprise risk management is a corporate method
thathasgainedimportanceininstitutionalboards,thankstoitsposi-
tioningasamanagementtool(Daviesetal.,2006)(BasakandShapiro,
2001).
Currently,thereareregulationsrelatedtostandardizetheefficient
management of organizations around their risks, such as ISO 31000
and ISO 22301. Whose purpose it is to integrate the best practices of
daily operations and apply them in wider aspects of the corporate
practices(Purdy,2010).
Themainbenefitsassociatedwiththeimplementationofthestan-
dards proposed by the ISO standards, transcend to (Purdy, 2010)
(Leitch,2010):
• Improvingefficiencyandgovernance.
• Developmentofconfidenceofthepartiesinvolvedintheuseof
risktechnicaltools.
• Application of controls systems to risk analysis in order to re-
ducefinanciallosses.
• Improve the performance, profitability and reliability of man-
agementsystem.
• Respond to the proposed change and the environment effec-
tively.
For the realization of the ERM processes, it is necessary to go
throughfourstages,whichare(BasakandShapiro,2001):3.3. EnterpriseRiskManagement−ERM− 47
1. Identification of the risk profile: Classification level of ap-
petiteoraversionpresentintheorganizationinordertoensure
all the efforts will be directed to the pursuit of goals, after the
understandingofthedifferentriskexposures.
2. ModelingandQuantification: Measurementusingmathemat-
ical tools or statistics previously identified risks, in order to in-
tegratewithbusinessperformancescenarios.
3. Risk Committee: Usually headed by managers in order to de-
terminethetolerancelevels(maximumleveloflossesaccepted),
considering the results of the modeling approach and recom-
mendations.
4. Monitoring of key risk indicators: Tracking the results ob-
tained after identifying disruptive and establishment of “risk
stoplights"tomanagethesituationstates.
The figure 3.2 shows the distribution of risk appetite according
to a series of colors (risk lights) empirically applied. The scale has
nothing to do with tolerance, as this will depend on the goals set by
theorganization.
The transition from green color to yellow color indicates the ex-
istence of a limit that is being crossing in order to take an action to
reduce risk (an example is the liquidity of financial institutions de-
scribed previously, which when it reaches the yellow color level is a
signal for the company that begins the analysis of a restructuring of
itsassetstructure). Suchactionsmaybeinsurancecontracts,creation
ofprovisions,salesofbusinessunits,amongothers.
The red color is outside of appetite, and immediate action is re-
quired, insurance contracts or the registration of provisions, is not
appropriatebecausetheriskismaterialandisengagingthebusiness
operation. It is also possible measurement, to get the quantification
ofprofitsorprofitabilitythroughmorespecializedmeasuressuchas
value at risk on operating results (Scandizzo, 2005), which will be
analyzedindeeplater.
3.3.1 Classifications of Enterprises Risk Management
Theevolutionofmarketsinwhichtheexchangeofgoodsorservices
arises,issubjecttointernalandexternalconditionsthatdefineitsop-
eration,makingthemwellsuitedfordemonstrationofriskscenarios
(BasakandShapiro,2001;Daviesetal.,2006). Thisiswheretheneed
for management tools designed to reduce the probable losses and
exposurelevelsofriskysystemsagainstmanifestationsarises.
Within the above context, we can identify some internal factors
affecting electrical markets, such as: the spot market price, financial
conditions, changes in regulations, investment, and the futures mar-
ket,amongothers.48 Chapter3. KeyRiskIndicators: KRI
FIGURE 3.2: Intervalsforriskappetite
Source:Computationsbyauthor
Similarly,externalfactorssuchassellingwholesalepowertomeet
the demand of a country or even the different forms of generation
that are linked to different processes for obtaining energy, are a re-
sultofthepresenceofdisruptorsasphysicalavailabilitynetwork,or
eventheuseofnaturalresourcesintheColombiancase,theterrorist
attacks to the infrastructure, climatic conditions, regulation modifi-
cations,amongothers.
In the studies carried out by (Medina and Manco, 2007; Beatty,
Ramesh, and Weber, 2002; Whited and Wu, 2006), it is possible to
identify that, the risk measurements have been focused on opera-
tional events. However (Domench, 2003) mention that there is a fi-
nancial risk component that should take a center stage as a result of
marketdevelopments. Thusthroughthepresentationofthischapter,
we intend to integrate financial developments and try to specialize
theanalysis
Now, unquestionably for financial issues, trading limits depend
on the initial conditions that allow to perform transactions, it means
that financial situations are subject to the operation. In other words,
from the operational point of view there are a series of physical con-
ditions in order to ensure that the energy flow is not interrupted
(Krause and Arora, 2010), such as the good condition of the trans-
mission network and programming, but also considered a series of
intangible situations that without doubt affect supply, giving space
totheinclusionofthefinancialcomponent.
Thus appear the contingent liabilities (Medina and Manco, 2007;
Beatty, Ramesh, and Weber, 2002), related to the ability to honor the3.3. EnterpriseRiskManagement−ERM− 49
businesses acquired from energy market participants. To better un-
derstandthissituationwecanthinkintwoscenarios,anoperational
scenario or tangible and the other one intangible or non-operational
stage. The first has concentrated its development in studies of black
outs (Newman et al., 2011) as a phenomenon that ensures supply,
whilethesecondscenariohasbeenstudiedbyanalyzingtheplayers
butconsideringtheplayersinanisolatedway(Newmanetal.,2011;
Dobsonetal.,2007;OverbyeandWiegmann,2005)withoutintegrat-
inggeneratedlinksintheexchangeofgoodsandservices.
Forthefirstscenariothemostimportantmeasureistheprobabil-
ity of failure of the network thanks to a tangible event (power fail-
ures, failures in supply, machinery, climate, terrorism, etc.). In the
second scenario is contemplated the lack of administrative planning
for instance as a intangible event (bad financial measures, ethics, in-
formation,legalcontiditions).
Internal, external, tangible and intangible factors, all of them are
subject to the global dispositions and they impact the stability of
the system but with different severity (Whited and Wu, 2006). For
purposes of this research project the possibility of providing energy
service without restrictions can be threatened thanks to impacts of
international markets, intensification of conflict (terrorism), climatic
factors,naturalphenomena,amongothers,whicharedifficulttopre-
dictusingmodels.
Following this line, the risks can be classified according to their
speciesanddisturbingelementconsideringtheclasificationmadeby
(Hughes,Logue,andSweeney,1975)inthefollowinggroups:
1. Market risk: is one that is derived from adverse movements
in the economic variables belonging to the own market such
asinterestrates,exchangerates,pricesoffinancialassets,com-
modityprices,pricesofutilities,amongothers. Uncertaintyre-
garding the evolution of such indicators is resulting in the risk
fromthemarket.
2. Credit risk: it comes from the non-compliance of the obliga-
tionsofthepartiesinvolvedinthebusiness(debtor). Itistradi-
tionallyknownastheriskof"default"wherethecommitments
are not honored, despite the previous analyzes made to the
grantingofcreditquota.
3. Liquidity risk: in this classification we can aggregate all situ-
ations where companies are committed to their ability to meet
their short-term obligations. Liquidity is the weak of the pos-
session of resources readily available (liquid). This in turn can
bedividedintotwo:
(a) Market Liquidity: comes from the difficulty to convert
liquidassetsincashthroughoperationsperformeddirectly
onthemarket(salesofassets,pledge,lease,transfer).50 Chapter3. KeyRiskIndicators: KRI
(b) Financing (or cash flow): derived from the inability to
cope with short-term financial obligations and access to
fundingsources.
4. Legal risk: in this group all the elements associated with con-
tracts, tenders, billing and others that need to be signed and
that cannot be legally enforceable in subsequent stages, giving
spacetomaterializationofcontingencies.
5. Operational risk: all losses associated with inadequate man-
agement of processes, technical failures, human errors, and af-
fectation by damage to systems, among others. Studies for the
electricitysectorhavefocusedonthistypeofriskmanagement
methodologiesfordevelopingandforecastingbasedonhistor-
icalinformationandtheapplicationofnewtechnologies(King,
2001).
6. Reputational risk: directly associated with actions committed
by the company or by employees of the same, affecting the
image and therefore the good name that is incident on the or-
ganizational strategy. This type of risk considered breaches of
ethics,integrityandotherconditions,whichareagainsttheval-
uesofthecompany(Poweretal.,2009).
Thelastclassificationofrisksproposesavisionthatallowsframe
them thanks to its nature and source of perturbation. The figure
3.3, graphically proposes one scheme for the Enterprise Risk Man-
agement, considering different elements (Basak and Shapiro, 2001).
Here is possible to observe that operational risks become a group of
independentimportanceandfurthercomprisestechnologicalissues,
corporategovernance,andphysicalevents.
A second group from figure 3.3 refers to all financial elements
of management of monetary resources where market risk, liquidity,
creditandlegalareaggregatedgivingrisetoanewexclusivelymon-
etary classification, where any problem falls on the profits and re-
turns. Finally the administration of the managing entity proposes a
third group where the main components are maintaining the finan-
cial soundness and the preservation of operational efficiency (Basak
and Shapiro, 2001). It is possible to note that in this proposal of
scheme, the management is not the center, while supervision based
onrisk,picksupeachcomponent.3.4. Keyriskindicators(KRI)derivedfromcorporatemanagement
51
andwithapplicationtotheenergysector
FIGURE 3.3: Proposal Scheme for Enterprise Risk
Management
Source:Computationsbyauthor-(Jorion,1996)
3.4 Key risk indicators (KRI) derived from cor-
porate management and with application
to the energy sector
Therehavebeenmanystudiesdedicatedtounderstandingperturba-
tions and the subsequent generation of indicators applied to the en-
ergysector(RennandKlinke,2004;HertzandThomas,1983;Sioshansi,
2002). However the vast majority of indicators have been concen-
trated on the understanding of operational events with the respec-
tive impacts on financial statements. Nevertheless and from studies
developed by (Parmenter, 2015; Krause and Arora, 2010; Lam et al.,
2006) and derivatives of this research proposal, It can set two large
groups that can be called macro key risk indicators and micro Key
riskindicators.
The former have a global origin of the whole system and there-
fore are related to each functional element seen as a universe, on the
other hand the second ones have an internal source from each par-
ticipating agent and therefore its management is the responsibility
of the same agent. This classification has a specific purpose and is
the establishment of risk inductors, it means which of the compo-
nents generate risk, under the top-down analysis (external) and the
bottomup(internal).
According to studies conducted by (Domench, 2003) in 2003, the
financial risk indicators applied to the energy industry, come from52 Chapter3. KeyRiskIndicators: KRI
traditionalpatternsthatfocusoncorporatemanagementoforganiza-
tions. Thus the assessment of solvency, liquidity, credit, financial ca-
pacity,amongothers,areimportantforthemanagementofthesector
(Domench,2003). Fromtheresultsof(Domench,2003)andthanksto
the contributions derived from this research process, the following
classification of indicators includes the initial proposals and others
identifiedthroughourreview.
Unattended demand cases, have taken place in the Colombian
market duringthe last years, more than 20events that have notgen-
erated blackouts, but those cases have generated alerts on the value
oftransactions. Thesizeofthecontractsisoneofthemostimportant
conditionsanalyzedbytheregulator,that’sisthereasonwhy,oneof
themostimportantconstrainsisthecapitalcapacity.
Theobligationsforoperateintheelectricitymarket,aredescribed
in the Decree 2119 of 1992 law while the regulator does not specify
financial risk with respect to what should be the conditions of the fi-
nancialratios. onlythefinancialcapacityofcapital(corecapital)and
some indicators VaR established in the regulation. In the chapter 4
with the inclusion of CROM and financial capacity, we are consider-
ingtherequirementsproposedbyregulator.
3.4.1 Macro key risk indicators
With the proposed classification made above, the macro key risk in-
dicators that respond to the environment and their characteristics,
arelistedbelow:
Percentagedistributionofenergyportfolio
Thisindicatorriskarisesduetotheneedtounderstandhowitworks
the structure of power generation in each country or region from
different resources (Awerbuch, 2006). That is, if the energy comes
fromdifferentsources,hydro,wind,solar,photovoltaic,thermal,nu-
clear, among others, since the risk exposure levels are different in
every form of generation. For example generation concentrated on
renewable sources such as water (hydro) has a high dependence on
weather phenomena (perturbation) while the thermal generation is
verysensitivetotheavailabilityoffuels(coal,oil,etc.).
Financialhedges
Are made from the use of financial derivatives intended to control
exposure to market risk. This risk indicator tries to identify which is
thevolumeofuseofhedgeswiththeaimtohighlightelementsunder
management and the risk tolerance possessing managers in front of
theagents. Thiswayifthecompanyhiresderivativestohedgeprices
for raw materials, interest rates, exchange rates, and other variables;3.4. Keyriskindicators(KRI)derivedfromcorporatemanagement
53
andwithapplicationtotheenergysector
then their tolerance level is low, but not always a dynamic strategy
ofhedging,improvetheresultsoftheyields.
Although it is not the scope of this project, to measure the ef-
fectiveness of hedges, we must emphasize that these financial tools
serveasaninputtoreducemarketriskintheoperation. Manyforms
of energy generation are exposed to commodity prices as thermal
energyorgenerationusingfuelvias(coal,gas,oil)andtherefore,the
companymusthaveadequatecoveragepolicy.
VARofenergyportfolio
Value at risk −VAR−, calculated based on the energy portfolio and
energy scheduled for dispatch (Chan and Gray, 2006; Liu and Wu,
2007a). This process is performed to obtain an economic estimate of
potential losses that could arise as a result of movements of some
variables in the operation (Liu and Wu, 2007b). It can apply many
measuresderivingthelevelofriskexposurethatisassumingabusi-
nessandoneofthemostrelevantthatisappliedininternationalmar-
kets is the VaR (Value at Risk) (Dahlgren, Liu, and Lawarree, 2003).
The energy sector adopts the method in order to establish whether
there are deviations from the energy scheduled at the beginning of
the day for be dispatched. In the Colombian case, if there are devia-
tions around 5% of the programmed energy, this will involve penal-
ties by the operator and those penalties will fall in the power gener-
ator having problems with the dispatch (Denton et al., 2003). Many
studies have been developed for many years in order to understand
the risk exposition in electricity markets (Liu, Wu, and Ni, 2006; Liu
and Wu, 2007b; Chan and Gray, 2006; Dahlgren, Liu, and Lawarree,
2003)
Blackouts
The phenomenon of blackouts has a lot of important implications
for economies as they can be classified as a brake on the productive
machinery. Therefore the recent studies on the stability of the en-
ergy system openly concentrated in the understanding of this phe-
nomenon (Wang, Grebogi, and Baptista, 2016). They are classified in
thegroupofoperationalriskandhavebeenstudiedthroughtheuse
of mathematical techniques, statistics and even innovative method-
ologies such as artificial intelligence or complexity (Dobson et al.,
2007). Thus the possibility of prevent the blackouts, can even antic-
ipate the generation of global losses due to the detailed study of the
network and its degree of exposure. The results found by (Newman
et al., 2011) defined the network as a complex dynamic system with
manyoperationalinteractionsthatcanbesimulatedtoestablishwith
anydegreeofcertaintythedegreeofriskexposure,soastoallowfor-
wardamitigationplan.54 Chapter3. KeyRiskIndicators: KRI
3.4.2 Micro key risk indicators
Theconcentrationofeffortswithinorganizations,relatedtothemiti-
gationofrisk,candecreasethedegreeofcomplexityassociatedwith
the operation of the electric system in some level. It is the company
or agent, an important element in the performance of the market
that has its own dynamic, independent, with self-learning and he
isevolvingthroughexperience(Boccara,2010).
Thatsaid,theinternaldynamicsoftheagentsrespondstoasystem-
integration process and therefore should not be treated randomly.
Thus, arises the micro key risk indicators associated with the evolu-
tionaryprocessofthecompanies.
VARappliedtothefinancialresults
Consideringthetechnicalinmathandstatistics,wecanmeasurethe
maximumeconomiclossprobablygeneratedinatimehorizonprevi-
ouslydefinedandbasedoncertainconfidence. Itisapplicabletoany
type of good, resource or asset that generates yields (Jorion, 1996).
For the operation of the electricity market is a probable loss after in-
vestments. Fromcorporatepointofview,isalossifweareconsider-
ingtheintegrationofallfinancialvariablesthataffectthenetincome;
even if the energy is not dispatched, this is a source of net loss. The
standard deviation is contained in the analysis of historical data or
profitabilityofinvestments,andisanalyzedindependently.
The calculation of VaR considering the definitions given by (Jo-
rion,1996)canbesummarizedbythefollowingexpression:
VaR = −W (R∗ −µ) (3.2)
0
Being:
W : InitialInvestment
0
R = rate of return for the period with mean µ and standard devi-
ationσ
Andthen,
W = W (1 + R), the value of the investment at the end of the
0
analyzedperiod.
W∗ = W (1 + R∗), is the lowest value of the investment at a level
ofconfidence“c".
R∗ =criticalperformance.
Where,
The absolute loss related to the initial value is calculated and an-
alyzedbasedonthefollowingequation(Jorion,1996).
VaR = −W ×R∗ (3.3)
0
Thus, the VaR depends on a probability distribution associated
withprofitabilityR∗ isafunctionofRandaleveloftrustestablished3.4. Keyriskindicators(KRI)derivedfromcorporatemanagement
55
andwithapplicationtotheenergysector
atthebeginningoftheanalysis"c"fromfigure3.4. TheVaR,insum-
mary is the expected value of the loss when a result exceeds the first
value.
Therefore, the results mathematically can be calculated based on
thefollowingrelationship:
(cid:90) R∗
P(R ≤ R∗) = f(r)·dr = 1−c (3.4)
−∞
Thefigure3.4canrepresentthebehaviorofvaluesaroundanav-
erage result (expected) and the risk component where R* is a critical
profitabilitythatcomesfromdeexpectations.
FIGURE 3.4: Probabilitydistribution
Source:(Jorion,1996)
One of the problems that have this risk indicator is the assump-
tionthatassetreturnsaredistributedaccordingtoadistributioncurve
standardized probability (Jorion, 1996) but in practice this is not en-
tirely true. Nevertheless the problem of aggregation of risks (those
that affect the profitability) is diminished based on the assumption
ofnormalitythatallowsaddthemthankstotheassumptions.
Earningsatrisk−EaR−
Is a methodology used in risk management of companies, and is
considered as a tool for quantifying exposure to market variables
(Chaffai and Dietsch, 2015), which has subsequently been special-
izing thanks to the inclusion of operational risks. It is defined as
the maximum likely net loss considering the behavior of disturbing
variables that generate risks in the various accounts that make up
the income statement. The result depends on two phases present in
net profits, a first operational phase (which comprises up operating
profit) and a second financial phase (which includes interest rates56 Chapter3. KeyRiskIndicators: KRI
on loans, exchange rates and valuation of financial assets) (Manco,
Botero,andMedina,2016).
In parallel with the methodology CFaR (Cash flow at risk) its de-
velopment has evolved because for the companies the issue of un-
certainty it is critical because of the high volatility stemming from
macroeconomic variables, which become in disruptor and generate
exposure. Thus, to meet these new requirements, some changes are
made to traditional VaR, because models initially only considered
theriskofassets(ChaffaiandDietsch,2015).
Operatingearningsatrisk−EBITaR−
Operating profit at risk or the EBITaR, can be defined as the maxi-
mum losses from the operational point of view that can present the
Ebit (operating income before interest and taxes) expected of a com-
panyandmayoccurwithsomedegreeofprobability. Thedifference
betweentheEBITaRandEaRisthatforthefirstriskexposurescome
from perturbations that impacting revenue accounts, costs and ex-
penses while in the second there is an additional element associated
withinterestrates,exchangeratesandnon-operatingevents.
The Figure 3.5 is a graphical interpretation for the EaR presented
by (Valencia, Jaramillo, and SAESP, 2010) in its research on the evo-
lution of EaR for trading energy companies in 2002. The calculation
of EBITaR and EaR evolves similarly although as mentioned above
the first exposure is associated with perturbations presented in the
income and expenses while the second includes all components of
net income considering interest rate debt, exchange rates for invest-
ment in currencies different than the functional currency, exchange
rates of liabilities, market valuation of financial assets, impairment
tests,amongothers.
FIGURE 3.5: DistributionofEaRandEBITaR
Source:(King,2001)3.4. Keyriskindicators(KRI)derivedfromcorporatemanagement
57
andwithapplicationtotheenergysector
Moreover,deviationofriskcanbeestimatedasthedifferencebe-
tween the value of the average of the distributions of the operating
profit (EBIT) or of expected net profits, and the maximum loss that
thanks to the influence of critical variables could occur estimated
thosemarketvariablesandsimulatedwithaconfidencelevelof95%
(Gómez-Bezares,2010).
The implementation of these key risk indicators can decrease the
riskthatthecompanygeneratesunexpectedfinanciallossesthatcan
add volatility to their earnings generation and in the other side the
value of its assets. In turn with the inclusion of tolerance, it can gen-
erate a tool very relevant for the administration because the equity
requiredby the regulatory systemas collateral to ensure compliance
oftransactionscanbeachieved(ZhaoandKang,2015).
DurationGAPbetweenassetsandliabilities−DGAP−
The concept of duration is very useful because it is a risk indica-
tor that measures the change in value of certain asset and liabilities
againstchangesintheinterestrate. Itisdefinedastheweightedaver-
ageofthedifferentmaturitiesoffuturecashflowsonaninvestment,
taking as weights the relative weight of each flow factor regarding
the final assessment or sum of the flows to present value (Barreira
Turnes, 1995). Mathematically, it comes from the first derivative of
pricewithrespecttotheinterestrate.
Similarly, it is possible to immunize investments, which refers to
decreasingthedifferencebetweenthedurationofdepositsininvest-
ments (e.g. operative life of one machine) and the duration of the
obligations (loans, bonds) in order to protect the deposits of capital
against changes in interest rates. Because the decline in asset prices
thanks to an increase in interest rates, will be more significant for
those positions with the greatest difference in the durations, it mean
lessimmunized.
A company and its set of assets, is a portfolio with different re-
turns, maturities and features. In the case of companies operating
in the energy market it is very common to see one gap between the
investment term and the term of the obligations acquired (Barreira
Turnes, 1995). This allows the mathematical development of finan-
cial instruments business for corporate risk management purposes.
Inthisway:
t
(cid:88) FCF
n
EV = ( (3.5)
(1+Wacc)n
n=1
Then,
t
∂EV 1 (cid:88) n×FCF
n
= − (3.6)
∂Wacc (1+Wacc) (1+Wacc)n
n=158 Chapter3. KeyRiskIndicators: KRI
Itmeans,
D
DModifed = − (3.7)
(1+Wacc)
Where,
• D=Duration.
• EV=EnterpriseValue.
• WACC=WeightedAverageCostofCapital.
• FCF=freecashflowofthecompanyestimated.
• n=projectionhorizon.
Withthisriskmeasurementmethodologythatfocusesonthebal-
ance sheet, it is possible to obtain an approximation of the exposure
of the market value of equity (equity value) against movements in
interest rates. However, this measure allows directly manage the re-
quirements demanded by the regulator of electrical systems related
tominimumavailablecapital.
Duration GAP - is the result of the difference between the dura-
tion of net assets (enterprise value) and duration of financial liabili-
ties(presentvalueofobligations).
VP
O
DModifed = D −D × (3.8)
NA O
EV
Where,
• VP=PresentValueoftheObligations.
• EV=EnterpriseValue.
Finally, the relative change of equity against changes in the inter-
estratewillbedeterminedbasedonthefollowingrelationship.
∂Equity EV(Wacc)
= − ×DGAP (3.9)
∂Wacc (1+Wacc)
Table 5.1 shows the procedure for determining the level of expo-
sureincompanieswithfinancial,thankstotheimbalancethatoccurs
whentheDGAPisveryhigh. ThuswhenDGAPisclosetozeroitcan
immunizethebalanceofbusinessandbythewaydecreasethesensi-
tivityofequitytochangesininterestrates,ensuringcompliancewith
therequirementstoparticipateinthemarket.
Finally,theimportanceofmanagingdurationsforcompaniesop-
erating in the electricity market lies in the need to have sufficient fi-
nancialstrengthtomeetthecommitments. TheoperatorinColombia
hasdefinedasystemforthemanagementofassetscalledtheCROM3.4. Keyriskindicators(KRI)derivedfromcorporatemanagement
59
andwithapplicationtotheenergysector
DGAP Changeininterestrate Changeinequityvalue
Positive Increase Decrease
Positive Decrease Increase
Negative Increase Increase
Negative Decrease Decrease
Zero Increase Zero
Zero Decrease Zero
TABLE 3.1: DGAP:Scenariosandsensitivities
for its acronym in Spanish (Buriticá Chica et al., 2014), and thereby
seekstokeepundercontrolthelevelsofequityinordertoenablethe
operationinstressscenarios.
Withthis,theassuranceofeconomicconditionsfromCROMgen-
erates adirect relationshipwith theindicator DGAP,given thatwith
thislatterindicatoritproposedacapitalstabilitythatallowsrespond
with the obligations. Thus the risk associated with interest rate is
limited,andbythewaycompliancewiththeproposedrequirements
bytheregulatorisachieved. TheDGAPandtheCROM,poseaclose
relationshipthatrespondstocorporatemanagement.
FinancialLeverage−FL−
The concept of leverage comes from physics and refers to support
point (Toro, 2004). In this case there are two main components that
are the sources of capital for use the assets. These sources are finan-
cial obligations to creditors (liabilities with cost) and its obligations
to creditors shareholders (Equity). The sum of these two sources of
fundingwillthereforenetassetsoftheoperation(NA)(Toro,2004).
Besides, the two sources for raising capital (debt and equity) are
fundingwithexplicitcost,itmeansisdonenotspontaneously(Damodaran,
1996). To understand the concept of spontaneous funding there are
forexampleworkingcapitalofacompany,whichmustremaininbal-
ance between short-term obligations (accounts payable) and short-
term availability (accounts receivable). In summary, financial lever-
age determines the financial structure of a company directly and its
cost.
Itisthen,
NETASSETS = Debt+E (3.10)
And,
NOPAT = Ebit×(1−Tax) (3.11)60 Chapter3. KeyRiskIndicators: KRI
NetIncome = NOPAT −Debt×K ×(1−Tax) (3.12)
d
Because only the interest are missing in the calculation of net in-
come.
NOPAT = Ebit×(1−Tax) (3.13)
Intheotherhand
NOPAT
ROCE = (3.14)
NA
Therefore,
NOPAT = ROCE ×(D+E) (3.15)
Andsolving,
NetIncome = ROCE ×E +D×[ROCE −K (1−Tax)] (3.16)
d
OnbothsidesdividingbyE
D
ROE = ROCE + ×[ROCE −K (1−Tax)] (3.17)
d
E
Where,
• NOPAT=Netoperatingprofitaftertaxes
• Ebit=Earningsbeforeinterestandtaxes.
• K =Costofdebt(interestrate).
d
• ROCE=Returnoncapitalemployed.
• ROE=Returnonequity.
• E=Equity
The return of assets deposited in a company depends primarily
on profitability regardless of the funding sources (Roce) and in sec-
ond place, the generation of value from operating profitability gen-
erated, because must exceed the cost of financing [ROCE −Kd(1−
Tax)]. Finally,thecoefficientassociatedwiththegenerationofvalue
is the degree of financial leverage, which can be interpreted in a sce-
nario"ceterisparibus"asfollows: ahigherdebt,higherreturn.
The great contribution of this kind financial solution for measur-
ing profitability and financial risk, is that there is not an optimal
point for which a company should contract the debt, but rather a
range (Toro, 2004). Similarly, the application in companies in the3.4. Keyriskindicators(KRI)derivedfromcorporatemanagement
61
andwithapplicationtotheenergysector
electricity sector is very relevant (Domench, 2003) because a highly
leveraged company can present problems of management and thus
givenegativesignalsthatlimitbusiness. InFigure3.6wecanseethat
the debt increases financial risk. Therefore there is a limit to which
thereturnindicatorsareimproved.
Debt
FinancialLeverage−FL− = (3.18)
Equity
FIGURE 3.6: Evolutionofdebtvs. profitability
Source:(Toro,2004)
Traditional theories suggest that the optimal financial leverage is
achieved from the relationship that maximizes earnings per share
(EPS) (Koller, Goedhart, Wessels, et al., 2010; Damodaran, 1996).
However from studies developed by (Toro, 2004) it is necessary to
consider a range of values regarding the structure to increase the
profitabilityoftheorganization.
Returnoncapitalemployed−ROCE−
The profitability that does not depend on the way it is financing the
company is called return on capital employed (Toro, 2004). And is
that under the scenarios, return not considered interest for debt or
dividends, hence its independence from capital sources. The defini-
tiondependsontheperformancerequiredofresourcesorassetswith
which the organization has to generate profits (Damodaran, 1996).
In the case of companies in the energy market these resources are
mostly tangible such as physical assets, power generation plants or
transmission network, but can also be intangibles such as goodwill
or recognition of know-how by the market thanks to the experience
acquiredovermanyyears62 Chapter3. KeyRiskIndicators: KRI
Itisthereturnoncapitalorinvestmentandisthemostimportant
for corporate monitoring, thanks to that calculate the generation of
value,establishingbusinessefficienciesordeficiencies.
NOPAT
ROCE = (3.19)
NETASSETS
Where,
NETASSETS = D+E (3.20)
The table 5.2 shows a scheme of financial balance, where the el-
ements that are part of the net assets are investments or capital em-
ployed. Fromtherightsideofthebalancesheetaredebtsandequity
while the left side functioning operational needs (FON) and compo-
nentsoffixedassets,itmeansthosewhosedurationisgreaterthan1
year.
FinancialBalance-NetAssets
Functioningoperationalneeds(FON) Shorttermdebt
Longtermdebt
FixedAssets
Equity
TABLE 3.2: NetAssets
Where, functioning operational needs are those resources with
which account the organization to ensure the normal functioning of
operations,inotherwordsthecashcycle
FON = accountsreceivable+providers+Acruals(Laboral,taxes)
(3.21)
WeightedAverageCostofCapital−WACC−
In the administration of the resources with which a company gen-
erates operating profit, there is an opportunity cost that relates to
theuseofsuchresources. Inotherwordsthemixoffundingsources
(debtandequity)resultsinthecostfortheuseofallassets,consisting
of contributions made by shareholders creditors and financial credi-
tors (Damodaran, 1996). In this regard, the cost of debt (K ) and the
d
equitycost(K )arethemaincomponentsofcostofcapital.
e
1. Costofdebt: referstotheinterestrateassociatedwiththeloans
and financial liabilities in general, where the charge is explicit
and that is made by the use of these resources capital through
theinterestrate(Koller,Goedhart,Wessels,etal.,2010). Among
thesetypesofsourcesofcapitalcreditsitcanincludeshortand
long-term bond markets, deposits, bankcards, leasing, renting,3.4. Keyriskindicators(KRI)derivedfromcorporatemanagement
63
andwithapplicationtotheenergysector
and other liabilities with interest rate explicit. One way to cal-
culatetheK isthiscalledhistoricalcost
d
Financialexpenses
Historicalcost = K = (3.22)
d
Financialdebt
2. Cost of Equity: Associated with the level of risk that an in-
vestor has when he deposited financial resources in the oper-
ation of a company through shares or equity interests. This
threatens the opportunity cost to a minimum return required
oncertaininvestmentthroughpreferencelevels,asinvestments
inotherassetsaremade. Theclassicmodelfordeterminingthe
K isknownastheCAPM(Capitalassetpricingmodel)(Koller,
e
Goedhart,Wessels,etal.,2010).
K = R +β ×(R −R ) (3.23)
r FreeRisk Market FreeRisk
Where
• R is the rate of return in the absence of risk (zero
FreeRisk
risk)
• R is the market return that contains the asset or in-
Market
dustry
• β is the proportion of systematic risk (not eliminated di-
versifying)
In addition to the above, the value of β will be greater if the
companyishighlyleveraged,itmeansifthecompanyhasmany
financialobligations.
After calculating the cost of independent funding sources (K ,
d
K )therelationshipbetweenthetwowillbeunderstoodastheweighted
e
averagecostofcapitalthatisassociatedwiththeuseofallassetsthat
come from these sources. In addition to the calculation of this re-
lationship it is important to consider the amount that the company
has in financial obligations and equity. WACC can be found by the
followingexpression(Toro,2004):
Debt Equity
WACC = ×K ×(1−Tax)+ ×K
d e
Debt+Equity Debt+Equity
(3.24)
Where,
• NetAssets=FinancialDebt+Equity
• 1 − Tax = Tax savings from the debt, the interest is tax de-
ductible64 Chapter3. KeyRiskIndicators: KRI
Finally for the company is strictly necessary to comply the fol-
lowingrelationinordertobeincomfortablepositionofprofitability:
ROCE > WACC (3.25)
Whichaddsaconstraintintermsoffinancialviabilitytobetrans-
ferredtotheexecutionofbusinessbetweeneachagentsystem,inthis
case each agent involved in the exchange of cash flows from energy
exchanges. Inthefigure3.7itcanclearlyseetherelationshipbetween
the level of weighted average cost of capital, cost of debt and cost of
equityrespectively.
FIGURE 3.7: Relationship between WACC and cost of
fundingsources
Source:(Damodaran,1996)
Solvency
It arises from relationship between the total resources owned by the
companyanditsfinancialobligationswithborrowersorgeneralcred-
itors. In other words, the number of times that the assets are in
the ability to respond for liabilities (Koller, Goedhart, Wessels, et al.,
2010). Thisrelationshipusuallyreferstothestabilityofmediumand
long term, because the assets are resources that can be exploited or
utilized in order to generate operative income over the life of the or-
ganization. Itiscalculatedbythefollowingexpression:
TotalAssets
Solvency = (3.26)
TotalLiabilities
The solvency indicator must be greater than 1x because in order
to determine the responsiveness, available resources in comparison
with the obligations, them must be clearly superior. Thus it is possi-
bletomeasurethecontinuityofoperationsinfinancialstressscenar-
ios, or in other words when corporate stability is threatened. Figure3.4. Keyriskindicators(KRI)derivedfromcorporatemanagement
65
andwithapplicationtotheenergysector
3.8showstheresultsofthesolvencyofthemainagentsoftheColom-
bian market during 2015, where everyone meets the initial require-
ment(greaterthan1)butthemeasuresarenotashomogeneous.
FIGURE 3.8: Solvency indicators in energy market in
2015forthemostimportantagents
Source:XM-Computationsbyauthor
Such indicators are one tool of financial management. In turn, it
isarelationshipoftwoextractedvalueswhichcomesfromthefinan-
cialstatementsorotherinternalreportformonitoring,withwhichit
seekstoformaconceptionaboutthecapacityofbusinesstohonorits
compromises in medium and long term. In the same way, such in-
dicators do not say anything for themselves, it is necessary compare
themwith:
• The industry average The average value of the industrial sec-
tor where the company operates. Each industry has its own
characteristics,whicharisefromtheexerciseoftheactivities.
• The indicator of previous periods The average or the trend of
previous periods, gives an idea of progress and setbacks that
haveinthecompany,itmeanstowherethebusinessisheading.
• The objectives of the company Allows understand administra-
tive management over certain period of time, to achieve the
proposedgoals.
• Other indices of the company That have relationship with the
calculatedindicatorandthatmayhelpexplaintheirbehavior.
Liquidity
It can classify the liquidity as a branch of solvency in view that it
refers to the capacity to meet the commitments that have maturities66 Chapter3. KeyRiskIndicators: KRI
but in this case less than one year. These commitments can be ac-
counts payable to banks, suppliers, taxes, debts with shareholders
andshort-termlaborobligations,amongothers.
Withintheacademictexts(Koller,Goedhart,Wessels,etal.,2010;
Damodaran,1996)ispossibletofindproposedlimitsupperandlower,
given that in extreme scenarios, the company must be in the ability
to honor its commitments contracted. However this range depends
on the sector that is evaluated and the economic environment faced.
However,itisalsonecessarytostressthatiftheindicatorislessthan
1 the company presents liquidity risk, which establishes an immedi-
ateconstraint.
CurrentAssets
Liquidity = (3.27)
CurrentLiabilities
This indicator evaluates the company from the point of view of
liquidation (all the operations are canceled), instead of considering
it as a going concern, because the liabilities are not settled with the
liquidationofcurrentassets,butwithincomeearnedthesalethereof,
which may be higher or lower than the carrying amount. In other
wordstherealbusinesscapacityisdeterminedbythecashflowsthat
maybegenerated.
Someformsofinterpretationofthisindicatorcanbe:
• The higher the indicator, it’s better. (Criterion from the point
of view of the creditor as it is a signal that the company will
meet its obligations), however, from the point of view of the
company, if they have high liquidity ratios indicates that they
haveidleresourceswithhighopportunitycosts.
• From a management perspective, the index depends on the
propermanagementofhavingassetsbetweenprofitabilityand
risk aversion (risk tolerance). A conservative political, prefers
to maintain a higher indicator in order to decrease its liquidity
riskindex,however,thisadverselyaffectsprofitability.
• Thebestapproachistocomparetheindexwiththeobjectivesof
the company, the industrial average and the historical average
ofthecompany.
Thefigure3.9relatesthetwoelementsassociatedwiththestrength
of business to honor commitments, which can be cataloged in the
short term or otherwise, long and medium term. In turn, some indi-
catorsaimedtoimprovereturns,allowdoingmeasuresfortheinter-
nal and external risk, establishing the preferences at the moment of
makebusinessbetweentheagentsinthesystem.3.4. Keyriskindicators(KRI)derivedfromcorporatemanagement
67
andwithapplicationtotheenergysector
FIGURE3.9: Categorizationbetweenliquidityandsol-
vency
Source:Computationsbyauthor-(Damodaran,1996)
Indebtedness
Is the financial risk and is understood as the inability to respond to
theirobligationswithexplicitcost,itmeans,theobligationsthatthey
havecontractedwithaninterestrateassociated(Damodaran,1996).
In this vein in a single set it can integrate the liabilities of short-
term and long-term without the distinction made as in the case of
solvency. A very indebted company must generate sufficient oper-
ating income to meet interest payments plus principal payments of
obligations in certain moments of time depending on the payment
termsinitiallyagreed.
Usually bank loans have repayment traditional schemes where
contributions are made up of principal and interest payments, like
any kind of commitment to explicit interest rate. However, in the
case of bonds are figures known as "bullet" where interests are paid
during the period required, but the main are canceled at the end
(Bouchaud and Potters, 2003). Thus it is depending on the charac-
teristicoftheobligationandtheimpactonthecashflow.
A first approach to the capacity to manage financial risk arrives
fromcapitalstructure,definedastheproportionofcapitalthatcomes
fromequitycontributionsinrelationtotheproportionofcapitalcomes
thatfromfinanciallenders(Toro,2004).68 Chapter3. KeyRiskIndicators: KRI
Debt
%Debt = ×100% (3.28)
Debt+Equity
Equity
%Equity = ×100% (3.29)
Debt+Equity
Withtheaboveitispossibletoestablishhowexposedofthecom-
panyregardingitsfinancialrisk,becauseacompanywithahighper-
centage of concentration in financial creditors, have greater need to
generate operating profit to respond to the interests arising from the
liabilities. On the other hand a company with high concentration
ratio in equity must answer for profitability risk associated to op-
portunity cost required by investors. The indicator is calculated as
follows.
Netfinancialdebt
Indebtness = (3.30)
Ebitda
Here, the net financial debt is calculated by deducting from the
total gross debt (liabilities with cost) the value of the cash balance
available at the end of the period. Ebitda for its part is the operating
profit before depreciation and amortization; it means it is the best
approximationofoperatingcashflowwithoutdiscountingtheeffect
ofinterest(Toro,2004).
The indicator is analyzed in the number of times because mon-
etary units are canceled allowing the result be dimensionless. This
way if the indicator is very high means that the debt is well above
theEbitda,increasingtheriskofdefault.
Around the world there are entities responsible for assessing the
risk of companies that emit instruments in the public market (Saun-
ders, Cornett, and McGraw, 2006). Those rating agencies are con-
structing metrics in order to measure the overall risk assessments
comprisingfactorssuchasfinancialrisk. Thus,thankstostudiesde-
veloped by (Erb, Harvey, and Viskanta, 1996) in the 90’s, can be de-
termined that an adequate level occurs when the indicator is strictly
less than 4x. This result becomes an additional restriction of the fi-
nancial system to limit borrowing capacity, determining a limit for
obligations with explicit cost and ensuring the stability of transac-
tions.
Forelectricitymarketswheretransactionsaremadeasoftheneed
forenergydispatch,theanalysisofthecounterpartywithwhichbusi-
nessisconductediscritical,giventhatagoodassessmentallowsthe
generationofconfidencewhenrunningthebusiness.
Coverage
the coverage determination responds to the availability of financial
resources of the organization to meet its financial obligations (Saun-
ders, Cornett, and McGraw, 2006), but in this case only with respect3.4. Keyriskindicators(KRI)derivedfromcorporatemanagement
69
andwithapplicationtotheenergysector
to the interests and it is that cash disbursements for the payment
of the principal of the financial obligations do not pass through the
statementofincomeanddependonthegenerationoffreecash. Thus
the relationship between the generation of operating profits and in-
terests caused in the operation must be high to establish a good re-
sponsiveness.
IncomeStatement
OperatingIncome —
(-)Costofsales —
GROSSINCOME —
GeneralExpenses —
EBITDA —
Depreciation-Amortization —
OPERATINGINCOME(Ebit) —
(-)FinancialExpenses —
INCOMEBEFORETAXES —
(-)Taxes —
NETINCOME —
TABLE 3.3: RepresentationofIncomeStatement
Table 5.3 shows the schematic for the income statement, where
EBITDA is above of the interest, hence it’s requires the submission
of a financial balance between the two monetary amounts. That
is, if the operational results are close to the interests, then coverage
will be close to 1, materializing the existence of financial risk (Erb,
Harvey, and Viskanta, 1996). That said the ideal scenario is one in
whichthecoverindicatorishigh,whichensurescompliancewiththe
obligations and improves the overall risk position because the cash
flow does not discriminate sectors (Saunders, Cornett, andMcGraw,
2006). Thentheexpressionispresentedforcalculatingtheindicator.
EBITDA
Coverage = (3.31)
FinancialExpenses
From the results found by (Erb, Harvey, and Viskanta, 1996) a
minimum level of 2.5 that helps reduce the perception of risk in or-
ganizations is established. This level often becomes a "covenant"
or agreement with financial creditors to continue the risk rating as-
signed,andinthecaseofissuersinthemarket,quiteusefulforplace-
mentsdecreasingtheriskofpreferencefortheirTitles.
FortheelectricitysectorinColombiathemostrepresentativeagents
had the following behavior in 2015 according to Figure 3.10 related
to the coverage, allowing state that the overall market has stability
from the point of financial view, but again the results are not homo-
geneous.70 Chapter3. KeyRiskIndicators: KRI
FIGURE 3.10: Coverage for principal agents in the
Colombianenergymarket
Source:XM-Computationsbyauthor
3.5 Future works applied to new indicators
The measurement or evaluation is a fundamental part of the risk
managementprocess. Companiesmustbeginbyunderstandingthat
are taking risks and identify the need to add transparency and rigor
to the most important according to the characteristics. Similarly, it is
necessary to define the tolerance levels that are willing to take; ob-
jectives often are given when an effective organization for risk man-
agementiscreated(BuehlerandPritsch,2003).
Amid this evolution in risk terms that requires the integration
of all the business areas as well as all streams of the economy, it is
necessarytohaveevolvingtoolsandnewtrendsforaggregation. For
such purposes in the case of the financial sector, for example, Basel
III (Repullo and Saurina Salas, 2011) have proposed standards for
risk management solvency and liquidity by the entities that provide
brokerageservices,maketransactionsandcollectionofmoney.
Such has been the extent of those proposed by the Basel commit-
tee, which even have demanded stress test in many institutions, to
establish whether they have the ability to respond in the midst of
adverse situations presented by the market standards. This, thanks
to the recent financial crises that have led regulators to toughen the
conditions to operate the system (Committee et al., 2010), given that
many problems were triggered by permissiveness in the indicators
ofsolvencyorliquidity.
Basel defines a level of technical capital or capital called "Tier
1" which consists of the ordinary capital and additional capital that
does not depend on valuations and elements of difficult realization3.5. Futureworksappliedtonewindicators 71
in cash. After that, they consider the traditional measure of risk-
weighted assets, which responds to the measurement of each of the
elements of the assets and their situation against the risk. For exam-
ple the risk of the cash and equivalents may be zero but the risk of
derivativeinstrumentscanneverbezero. IntheindicatorTier1inall
scenarios must exceed 4.5% according to the regulation (Committee
etal.,2010).
Finally it can relate these two components (technical capital and
risk-weighted assets - RWA -) resulting in the basic indicator Tier 1
solvencyasfollows:
TechnicalCapital
Tier1 = (3.32)
RWA
Even the regulation goes further and proposes an indicator total
solvency which is calculated by the sum of Tier 1 and Tier 2, where
the Tier2, shows the relationship between the secondary capital (or
capitalthatisnotrealizable,whichcomprisingelementssuchasval-
orizations,hybridinstrumentsdebt-equity,subordinateddebt,among
others) (Committee et al., 2010). In turn, the sum of Tier1 and Tier2
must be above 8%, meaning that the total solvency must exceed that
value. Thankstothis,thefinancialsectorhasaglobalconstraintthat
controlstheevolutionofoperations.
The description above is a starting point for future risk measure-
ment. Since the risk in the corporate environment, defined as the
uncertainty present in returns and in future values of cash flow, de-
pends either on the characteristics of business associated with the
type of activity and on the other hand of market conditions (Com-
mittee et al., 2010). Therefore, the measurement requires a corporate
risk management method that is set to each type of business. Thus
for electricity market is possible to propose adjustments that related
theircapitalcapacitywiththeexposureofnetworkassetsusedinthe
operation, it means transfer some lessons from Basel in the compre-
hensivecontextofbusinessrisks.
Theseproposalsforintegrationandapplicationofmethodologies
have an explanation. For the regulator in the Colombian case, the
requirementsofminimumcapitallevelstoensurecomplianceofop-
erations are nothing new. Since the year 2012, there established the
CROM (Buriticá Chica et al., 2014) as part of this trend to set mini-
mum assurance capital requirements for agents involved in transac-
tions. The CROM is a direct application of Basel when calculating
technical heritage, which have been questioned with some factors
that can be reviewed, such as the inclusion of valorizations because
isaelementwithdifficultrealizationincash.
CROM is defined as a capacity of supports the operations on the
market for one specific agent, at a certain moment of time (Buriticá
Chica et al., 2014) and is expressed in kWh based on the value at
risk. On the other hand the value at risk for securing transactions72 Chapter3. KeyRiskIndicators: KRI
depends on the energy traded, the price of the contracts signed for
the dispatch of energy and the scarcity price. The latter indicates
the value to which must be paid when the obligations of energy are
required.
With all this, the integration of more elements for the study of
risks identified in the energy sector, allows to enrich the analysis
ahead of evolution in the sector. The new proposals, will achieve a
certainlevelofimportanceconsideringthecollectionofcomponents
from other sectors such as finance, in order to ensure the operations
andsystemstability.73
Chapter 4
Modeling Electricity Markets
from a corporate perspective
4.1 General overview
Theenergymarketadministrationconsiderssurveillanceofbusiness
transactions of energy, its transport and delivery to final customer,
enhancing the exchange of services between participants and ensur-
ing cash flow through account management. One of the functions
delegated to process of market administration is the portfolio man-
agement and trade recording of transactions in accordance with the
dispositions of the regulation. According to this, this chapter is the
approximation for ensures the transactions considering the financial
equilibriumbetweenagents.
Playing a physical phenomenon through mathematics is in most
cases a rather complex process, thanks to the number of variables
involved(Boccara,2010). However,thishasnotstoppedtheprogress
of science, because the progress is reflected in problems expressed
bysimpleequations,orwithlessquantityofparametersinvolvedas
relativity,gravityorkineticdynamics,amongothers.
Althoughoftenarethesemathematicalexpressionsconsideredas
a simplistic approximation of reality, which is present in the laws of
nature(SoléandManrubia,2009);itisaresponsibilityofresearchers
to conductthe necessary tests, summarizing such laws or somephe-
nomenaalthoughthereisnoabsolutecertainty. Thisobligationarises
fromthecommitmentthatsciencehaswithhumanityandisdelegate
fromgenerationtogeneration.
On the other side, social and economic sciences have been clas-
sified on a branch devoted to administrative management of com-
panies and nations. For this reason, advances in research are not as
crucial for development of humanity as are those results through bi-
ology, chemistry, physics or mathematics. In other words the social
andeconomicsciences,withalotofcomplexproblemstosolve,have
alaggardpositioninitsscientifictreatmentincomparisonwithother
sciencesareas.
In this sense, finance is the result of a specific necessity of mon-
etary control associated to countries, entities, individuals and worldChapter4. ModelingElectricityMarketsfromacorporate
74
perspective
order(Damodaran,1996). Nevertheless,adevelopmentinthefinan-
cial or economic field will not be decisive in the life expectancy of
people as can be the discovery of a new vaccine, the treatment of a
disease or even the study of the origin of the universe with the aim
ofunderstandinghumandynamics(Kwapien´ andDroz˙dz˙,2012).
But the research may propose a different way of doing things,
after reviewing alternatives, not necessarily a better way but defi-
nitely different. The economy and finance of the companies are con-
nectedin thisresearchproposal, allowingthedevelopment ofanew
methodology for action in everyday processes. Specifically the con-
struction of this thesis concerns the description of the physical phe-
nomenon associated with financial transactions that take place daily
intheenergymarket,expandingsystemicrisk(Newmanetal.,2011).
Therefore, this chapter is intended for the construction of mod-
els that describes the financial phenomena. Presenting an optimal
result that establishes a new way of doing business under different
constraints, and in absence of regulatory changes. In this way, the
use of game theory, proposed by Morgenstern and Neumann (Neu-
mannandMorgenstern,1947)subsequentlydeepenedbyNash(But-
tler and Akchurina, 2013) is the first approach of modeling that we
used in the first approximation by game theory. Secondly, the ad-
justed model is based on the theory based on agents (Krause et al.,
2006)andcomplexitystudiedby(Boccara,2010)inphysicalsystems,
in the second model, we use the proposals through the description
of physical phenomena. This model is integrated with elements of
simulation and optimization, and it will be a tool that considers the
interactions between agents in seeking to ensure the stability of the
system,fromthestrictlyfinancialpointofview.
In summary we are taking the definitions given by (Buttler and
Akchurina,2013)(Boccara,2010)(Krauseetal.,2006)(SoléandMan-
rubia, 2009) in order to construct an integrated model that considers
many variables from the financial process, and thereby describe the
physicalbehavior.
It should be noted that the applications that are made in this in-
vestigation have collected particularly the dynamics and the market
organization, and also, a number of elements that impact the daily
evolution. Howevermanyotherelementsareoutsideoftheanalysis
becauseoftheconnectionoffactorsismorecomplex. Suchisthecase
ofblackouts,maintenanceschedule,andexternalriskfromdisasters,
climatic variables, generation portfolio forms, asset availability, and
regulation, among others (Apt et al., 2004). The figure 4.1 shows the
scheme for internal and external components that affects the com-
plexityofthesystem.4.2. Firstapproximationtothephysicalphenomena 75
In the figure is possible to appreciate the diagram proposed in
general for electricity market, and outside the scheme, the different
variablesthataffectstheoperation. Externalfactorslikeinternational
markets, climatic events; internal conflict (in the case of Colombia,
the war that allows, terrorist attacks to infrastructure) and economic
crisis,amongothersareconsideredintheoperationalriskmeasures.
The electricity market has an integrating role for all transactions
as it brings together all agents and more than 80% of the energy is
negotiated through contracts with fixed prices. In turn, the timing
of review of such contracts depends on the financial analysis of the
agents and is estimated to occur on a quarterly basis. All this is cru-
cialintheconstructionoftheobjectivefunction.
Finally, although the results from this research are financial and
economic, cannot rule out the integration of such operational ele-
ments. Thereby an interaction between the financial model and the
operationalmodelinthefuturerepresentsamorecomprehensivere-
sultassociatedwithmanagementandmarketstability.
FIGURE 4.1: Components that affects the complexity
ofthesystem
Source:Computationsbyauthor-XM
4.2 First approximation to the physical phe-
nomena
To describe specific phenomena, is in many cases a complex task.
It means, even only using words for explain the behavior or the
causes could be difficult if the analyst doesn’t understand the pro-
cess from the beginning to end. In some cases the uses of literatureChapter4. ModelingElectricityMarketsfromacorporate
76
perspective
or researches are a good approximation in order to understand the
process, which will be explained, but is necessary to in many cases
theexperienceoftheexpertswhenstarttheprocessofinterpretation.
The figure number 4.2 is a synoptic approximation of the finan-
cial physical process through a mental map. The goal is the profits
maximization but there are different considerations for the electric-
ity markets specifically. The scheme in the figure, represents exclu-
sively the financial problem, which considers uncertainty around of
the decision process. As a whole there are many variables involved
butfinanciallyitstartswithforecast,determinationofenergyneeds,
precios, quantities and finally, financial statements, it means profits.
Variables like the financial problems with other agents, regulation,
and climatic conditions, geopolitical affairs that affect the prices un-
der diverse scenarios of demand. The uncertainty appears from op-
erational conditions, the methodology applied in the demand fore-
cast, and in general from all the information used for the agents at
themomentofparticipatedinthemarket,asabuyersorsellers.
FIGURE 4.2: Causesandeffectsoftheproblem
Source:Computationsbyauthor
The studies in the electricity markets have been concentrated in
theproblemofassurancethesupplyfromthegeneratorperspective,
itmeansproducersandoptimizationcapacity(Borenstein,Bushnell,
and Knittel, 1999). This research project is focused on the behavior
of traders and producers, and the assurance of the supply of energy
butnotfromoperativeperspectivebutratherfromfinancialcapacity
viewpoint. Thisisthemostimportantcontributionofthiswork.4.3. FinancialstabilityusingGameTheory 77
Inequilibriumthegoalistoidentifythequantityofenergytraded
of each agent for ensuring the maintenance of the system, maximiz-
ing its profitability (Heusinger, 2009). This is the first part, and the
second part is to consider the capability of each one for buy energy,
evaluating different indicators like a financial risk, solvency, liquid-
ityandexposuretodifferentvariableswithuncertainty. Also,evalu-
atetheconditionstomakebusinesswiththecounterpart,measuring
its capital position and its financial support in order to honor the
compromises.
The demand is independent between agents (buyers - sellers of
energy)(Bohi,2013)andtheymustdecidehowmuchenergyshould
seek to reach the demand programed at the beginning of the day,
while minimizing costs and maximizing the utility with less uncer-
tainty. InthisstudythedemandisassumedasaPoissonprocessbut
in the future will be possible integrate another researches that will
improvetheresults.
Inotherwords,themechanismoftheelectricitymarket,function
asagame,whereitispossibletoidentifytheplayers,thepayofffunc-
tion, actions, strategies and the equilibrium. All of the components
comefromaperfectcompetitionassumptionandinthemiddleofan
oligopolisticenvironment.
4.3 Financial stability using Game Theory
Throughout this section the energy market as represented as a game
in normal form. A game in the classical form consists of (1) play-
ers indexed by i = 1,...,n, (2) strategies or more generally a set of
strategiesdenotedbyx ,i = 1,...,nperformedtoeachplayerand(3)
i
payoffs or utility function π (x , x , ..., x ) , i = 1,...,n won by each
i 1 2 n
player. EachstrategyisdefinedonasetX ,x ∈X ,andaccordingto
i i i
(Camerer,Ho,etal.,2015)theCartesianproductofX ×X ×...×X
1 2 n
is called the strategy space. Each player may have a unidimensional
strategy or a multi-dimensional strategy depends on the level of in-
teractionwiththeotheragentsandtheexpectationsofprofitability.
A one-way selection of strategies in the normal form also can be
designed in the extensive form as an alternative to the formal form
ofgame;itmeansmoreinteractionsandpayoffs(Camerer,Ho,etal.,
2015). So, sequential choices are possible and players may learn in-
formation between the selections of different actions, particularly a
player may learn which actions were previously chosen or the out-
comeofarandomeventbutinthespecificgameitisnotsocommon.
Agents can learn like in the Bayesian case, however in this propo-
sition, they can learn from the bad financial indicators provided by
participantsconsideringfinancialinformationavailable.
When simultaneous moves are repeated in stochastic games, if
two players or more take actions in multiple periods, it can create aChapter4. ModelingElectricityMarketsfromacorporate
78
perspective
different type of dynamic game. And in the case of energy markets,
the decision of buy or sell energy are performed in one specific pe-
riod. For example the inventory models used in SCM (Cachon and
Netessine, 2004) considers replenishment of goods and the decision
forbuyaremadeoverandoveragaininmultiperiodsgames,which
is not the case of electricity markets. Two major types of multiple-
period games exist: without and with time dependence (Gibbons,
1997).
In the multi-period game, the strategy for each player is the se-
quence of actions taken in all periods. In contrast with electricity
markets, for decisions in order to reach the demand level at the be-
ginningoftheperiod,theyhavetodecide,inshortagescenarios,how
much energy should buy (Malandrino et al., 2015). And how much
energycansellinsurplusscenarios. Thedemandisrealizedandthen
leftover inventory is not necessary to be salvaged (Bohi, 2013). But
thelastsalesandbuysaretakenthroughstockexchangebecausethe
contractshavebeensignedpreviously.
FIGURE 4.3: SchemeoffictitiousAlgorithm
Source:AccordingdefinitionsgivenbyYousefi,Moghaddam,andMajd,2011
Figure number 4.3 is a representation of fictitious game where
the agents can learn considering the experience of interaction and
history (Yousefi, Moghaddam, and Majd, 2011). Agents using the
information determined the most likely strategy or best response in4.3. FinancialstabilityusingGameTheory 79
front of others that maximize the profits. Looking forward the situa-
tions,agentswillimplementstrategiesandconsideringtheresultsin
thenextstepofthegame(day,month,year)theagentsgoingtotake
thesamestrategyordifferentstrategies.
So, the energy market is a game that is not a zero sum, because it
is possible to generate surplus from the first demand and must sup-
ply energy to others traders that buy, in comparison with the initial
situation(Xiaoetal.,2015). Itmeanstheagentscantradeenergy,but
in order to accomplish the compromises of dispatch, they must buy
orselltheshortageorthesurplus.
On the other hand, according to the explanation of the variables
in the fictitious game, we present two variables in order to describe
thesituationoftradersintheelectricitymarket,buttakingconsider-
ationsofthegeneralgame:
x = is the strategy of each trader where the amount of energy is
i
definedtobuy,butconsideringthequantitythatthecounterpartcan
sell,inotherwordsaftertheanalysisprocesswhichmadetheseller.
Utilityorπ =profitorpayofffunction,istheoutputanddepends
i
onXandactionstakenaround,tonotgeneratelosses.
There are many variables that affect the system but we consider
the most relevant in this case, the strategies and the quantity x for
i
eachtrader,whichsumshallbethetotalpurchases.
The uncertainty comes from two aspects: energy demand and
competitors because at the initial situation is not easy to know the
strategy that will advance each trader, in other words the quantity
of purchased energy, because could be less or more than the initial
demandprogram(WeidlichandVeit,2008;Wolfram,1999).
Thedemandforeachtradercomesfromthestrategyandthechar-
acteristicsofthebusiness,abigtradercanhaveabigdemandandin
the same way for small and medium traders. The figure 4.4 shown
the interactions between the agents, which have the possibility of
buyorsellenergyaccordingthedemandlevel. Thecentralregulator
has the responsibility of ensure the operation of the market and the
complianceofthedemand. Eachprogramofdemandisanewgame,
that’s why the fictitious game can be established daily, monthly or
annually.
The supply has a statistical distribution, is assumed known to
represent the possible values taken at one point in time (monthly,
quarterly,annually),followingthemethodproposedby(Cachonand
Netessine,2004)andusuallyindifferentmarkets,dependofthegen-
erationsources,likehydrologic,nuclear,solar,kinetic,amongothers.
Eachtraderwantsthequantity“x "tomeetthedemandrequests.
i
Iftherearemissingshouldlookforanothertraderinordertosupply
the required amount at a cost of rescue (recovery price), the trader
buysatacost“c "andsoldatapricep .
i iChapter4. ModelingElectricityMarketsfromacorporate
80
perspective
FIGURE 4.4: Visualizationofinteractionsituation
Source:Computationsbyauthor
Given that the problem is a market problem there is no storage
costs because the energy must be dispatched at the time and the
agents cannot save the energy. Lost sales cannot be recovered and
there is no replacement of missing. The regulator is responsible for
monitoring the compliance of transactions between agents, guaran-
teeingtheoperationandthusensuringthedailydemandofthecoun-
try. Asweshowedinthefigure4.4.Theregulatorproposesoperating
rules and agents must follow this rules in order to continue partici-
patinginthemarket.
Theonlysharedgoalistomaximizetheprofitsofthesystemand
for each trader maximize its own profit. An energy dispatch in time
tisavailableimmediatelyandhastwomomentsofdecision: thefirst
is the time to choose how much energy purchased to face the mo-
ment of occurrence of demand. The second are transfers of surplus
and coverage of missing that occurs after accomplish the satisfac-
tion of the demand and is the result of transactions between agents,
whichisnon-cooperativegame(Gibbons,1997),andconsideringthe
development in the middle of a cooperative situation (to sell or buy
in order to maximize the profits), that’s why is guaranteed the algo-
rithmconvergence. Thedefinitionsare:
• N:Numberoftraders.
• A:Setofactionstotakeeachtrader,powerpurchasedecision.
• c : Costforunity($/kwh).
i
• s : Sales.
i
• x : Energypurchasedvector.
i
• p : Price($/kwh).
i4.3. FinancialstabilityusingGameTheory 81
• h : Surplus.
i
• e : Shortage.
i
• q , : energyneedsfromitojwheneachdemandarenotreached.
i j
Beingj otheragentdifferenttoi.
• m , : Transfer costs betweeniandj. Being j other agent differ-
i j
enttoi.
• v : Recovery value: is a value of the energy, that can recover
i
someofthecost(inColombiacanbescarcitypriceorminimum
pricedependsontheposition)
• L:Matrixoftransfercostsrepresentedthroughm , .
i j
• D:Totaldemand.
• de: DemandVectorforagenti.
• se: Salesvectorforagenti.
• he: SurplusVectorforagenti.
• ee: ShortageVectorforagenti.
(cid:88) (cid:88) (cid:88)
Ut = (p ×s −c ×x ))+ (p −v −(m ×q ))+ (q ×v ) (4.1)
N i i i i i i i,j i,j i,j i
The function could be divided into two parts: the first part is
the profit of each trader, which does not consider the maintenance
and inventory management, in other words the first stage of the
game. The second part involves the recovery of rescue values, plus
the amounts of energy transfer from gamer i to gamer j to supply
themissingdemand. Itisfromtheperspectiveoftheagent-receiving
surplusfromothertraderstosupplyshortages.
Thethirdfactoristhesurplusthateachtradersenttootherrecov-
ering rescue (recovery) value. The result is a Cournot equilibrium,
because competition is generated by the energy traded in a moment
oftime,inthiscasethesizeandfinancialcapacityofeachagentdoes
notreactfacingtheequilibrium. Theoptimalquantityis:
x∗ = x ∀ ∈ N (4.2)
i i
DemandduringtheprocessisarandomvariableD,withdistribu-
tionfunctionDF.InthiscaseDFisaPoissondistributionconsidering
the study of the demand in a fictitious game as (Cachon and Netes-
sine, 2004) and adopted in the research in order to find the Nash
equilibrium. Thegeneralprobabilityfunctionis:Chapter4. ModelingElectricityMarketsfromacorporate
82
perspective
exp−λλk
f(k,λ) = (4.3)
k!
Where k is the number of occurrences of the event. Is a positive
parameterrepresentingthenumberoftimesthatisexpectedtooccur
CachonandNetessine,2004.
The equilibrium is found through the inverse function evaluated
ataonepoint,thepointistheyieldobtainedbetweenthedifferences
in cost and price (Cachon and Netessine, 2004; Cure Vellojin et al.,
2009). Wecanfindthesolutionforthelevelofpurchasesx thateach
i
agent can make and is the inverse of the function of demand evalu-
atedintheprofitability.
(cid:18) (cid:19)
p −c
x∗ = F−1 i i (4.4)
D p
i
The trader’s decision variable x , while taking the competitors
i
strategy x as given the best response (Nash equilibrium). The best
j
response can be found, optimizing each trader’s payoff function, it
meansnetprofitfunctiondescribedbefore.
(cid:18) (cid:19)
p −c
x∗(x ) = F−1 i i ∀i = 1,2,3...N (4.5)
i j Di+Dj−xj p
i
Lastequationappliedinordertofindtheequilibrium.
Thevectorofactionsthatconsidersthebestanswersfromagents
is:
(cid:88) (cid:88)
x = (de+ ee − he ) (4.6)
i −i −i
In other words is a relationship between demand vector (initial
requirements), vector of shortages because is possible to buy less
quantity, and finally vector of surplus for selling to another trader.
This result is obtained for any instant of time where information
is known (daily, monthly, quarterly, annually) and these constraints
arise in order to limit transactions to energy needs. Traders and pro-
ducers are acting as a similar agents because finally the disposition
ofenergycomesfromgenerationplantsorfromthespotmarket.
Subjectto,(restrictions):
(cid:88)
q ≤ he ∀i ∈ N (4.7)
i,j i
(cid:88)
q ≤ ee ∀i ∈ N (4.8)
i,j i
It means that the amount of energy that need an agent i from an
agent j, in no case may exceed the surplus and also must be below
theshortage. Thusthesupplyofenergyisensured.
(cid:88)
x ≤ D (4.9)
i4.3. FinancialstabilityusingGameTheory 83
q ≥ 0;x ≥ 0;∀i,n ∈ N (4.10)
i,j i
In order to reach an optimum point, the objective is to find the
equilibrium between agents, with best response according to pur-
chasingprocess.
The vector of actions to be taken by each trader is the follow,
wherex representseachaction.
i
The scenario simulation is performed for a day of operation pro-
gramming, which requires the release of energy to final consumers
through retailers, whose responsibility is the fulfillment of such dis-
patchofenergy.
4.3.1 Optimization
Themethodusedforoptimizationoftheproposedmodelisthesim-
plexmethodinordertofindautilitymaximizationthroughitslinear
behavior(Vanderbei,2014). Ingeneral,theexpressionis:
Max(z) = CT ×x (4.11)
Subjectto
Ax ≤ b;x ≥ 0 (4.12)
We want to optimize the utility function, considering different
constraints, it means the quantity needs have a threshold definite
(he , ee ) and the non negative numbers, because the purchases cant
i i
belessthanzero.
Applyingthelastmathematicalexpressiontotheproposedmodel,
wheretheequationistherepresentationofutilityforeachagent:
Max[Ut (x)] (4.13)
N
The Simplex method is a method using the interaction with the
aim of gradually improving the final estimation at each next step
(Vanderbei,2014). Itisananalyticalmethodforthesolutionofprob-
lems whose main characteristic is linear programming but is in the
abilitytosolvemuchmorecomplexproblems,withoutinitialrestric-
tions on the number of variables. The final outcome rests on an ob-
jective function to be maximized or minimized as appropriate and
subjecttotheconstraintsidentified(Vanderbei,2014).
Nash equilibrium can represent an optimal scenario that ensures
the function of the market considering different constraints. But,
the equilibrium is not a obvious process because there are different
methodologies used in order to find it (Heusinger, 2009; Krawczyk
and Uryasev, 2000) and none of them are classified as the best. The
problemcouldbetheappearanceofdifferentscenariosorevenwhenChapter4. ModelingElectricityMarketsfromacorporate
84
perspective
thetimegoeson. Thelastaffirmationtakesrelevancebecauseimme-
diatelytheequilibriumproposedbyNash(Axtell,1999)andapplied
inthisspecificproblem,becomesunstable.
4.4 Model for measuring systemic risk for en-
ergy agents: General process and physi-
cal process using a complex aproximation
The expected return of an agent depends on the volume of transac-
tions and the ability to generate capital profits associated with the
purchase and sale of energy in the electricity market. In that way,
profitability, risk position, capital availability, adequacy of invest-
mentsintimeframes,liquidity,solvencyandthemanagementofthe
debt, specifically "outside capital" (financial liabilities with cost), are
variablesthatmustbeinpermanentevaluation.
There are different variables considered in the decision process
to buy or sell energy in the electricity market. Specifically from the
financial perspective, previously in the chapter number 2 it defined
themostimportantindicators,asasolvency,durationGAP,liquidity,
leverage,coveringandriskpositionamongothers.
It means, climatic variables, availability of generators, terrorism
attacks, regulation reviews, hedges applied on international prices,
international economic perspectives and others, are variables that
this model doesn’t consider in the financial risk evaluation context.
But for future researches it will be possible, it means all of the vari-
ablesrelatedtotheoperationalexpositionwillnotbeconsideratthis
time.
The figure number 4.5, is an adaptation from National institute
standardsandtechnology,consideringtheresultsdevelopedby(Babic,
2014) in relation with the optimal functioning of the energy sector.
But the results respond one question about the impact of electrical
grid systems from operational perspective. It is possible to see that,
there are outlines key entities and interactions inside the markets.
Theproblemstudiedinthisprojectisfocusedintradingandmarket
managementinsidethemarketdomain.
According to the last paragraph, this research is concentrated in
the description of the market modeling, considering only the finan-
cial exposure of each individual company and even consolidated as
a holding. There are parameters, constants, and variables that are
subjectofmodeling.
Theenergyisanassetclassifiedasa"utility-commodity"andfor
that reason is considered inelastic in the short term (Bohi, 2013), it
will be the first constrain in the model. The second important con-
straint is that, the energy does not distribute dividends during the
analysis horizon, because in this case the analysis are focused in the4.4. Modelformeasuringsystemicriskforenergyagents: General
85
processandphysicalprocessusingacomplexaproximation
FIGURE 4.5: Optimalfunctioningoftheenergysector
Source:Babic,2014
capacityofthecommoditytobetradedandthecashandequivalents
generated,thereforethedividendiszeroδ(t) = 0.
Is important to mention that the price p and the cost c are
t,i,j t,i,j
different, because depends on different negotiations process, in that
sense the problem is not a symmetric problem because all the condi-
tions are changing from contract to contract and the purchased en-
ergytooneagentisnotalwaystheenergysoldinthesamecontract.
In the same way, the quantity purchased from one agent, are not
the same quantity sold of other agent which he has business. It
means if one agent i buy energy from the agent j in the terms of
one contract, is not necessary the same quantity sold by agent j to
agentiinothercontract. Quantitiesareindependents.
• δ =0=Dividend
t,i
• p =Thepriceattimetforcontracts,consideredbytheagent
t,i,j
iforbuyenergyfromthetraderj.
• c = Cost of energy at time t for contracts, considered by the
t,i,j
agentiforsellenergytothetraderj.
• Q = Quantity of energy purchased by agent i from agent j at
t,i
timet,consideringthevalidityofcontracts.
• S = Quantity of energy sold by agent i from agent j at time t
t,i
consideringthevalidityofcontracts.
• Wacc =Istheminimumexpectedreturnattimet,costofcap-
t,i
italforagenticonsideringdifferentcapitalsources.Chapter4. ModelingElectricityMarketsfromacorporate
86
perspective
• kd =Interestrate,financialcostforagenti,attimet.
t,i
• Roce =Returnoncapitalemployedattimet,foragenti. This
t,i
returnisindependentofcapitalsources(debtorequity).
• OyM =Operativeandmanagementexpensesfromagenti,at
t,i
timetanditdependsonmanagementstrategy.
• h = Consolidated expected return at time t by agent i, h =
t,i t,i
Roce - Wacc . The value should be greater than 0% estab-
t,i t,i
lishingthegenerationvalue
• D =Totaldebtofagenti,attimet“outsidecapital".
t,i
• He =Quantityofsurplusenergybyagentiattimet.
t,i
• Ee =Quantityofshortagesenergybyagentsiattimet.
t,i
• pb =Spotpriceinenergystockexchange,thepricecomesfrom
t
themarketandchangeaccordingtodemandandsupplylaws.
• EBIT = Operating income after discount expenses and cost
t,i
byagentiattimet(Earningsbeforeinterestandtaxes).
• pz =Scarcityprice(givenbytheoperator)anddependsonthe
t
operativesituationofthemarket.
• pmin = minimal price (given by the operator) CERE + FAZNI
t
(Bogotáetal.,2011).
• VaR = Value at risk of financial operations form agent i, at
t,i
timet.
• E = Equity value composed by subscribed capital, reserves,
t,i
accumulatedprofit,valorizations,movementsonintangibleas-
setsandothers.
• SCOB =Supportcapacityofoperations,financialcapacityfor
t,i
operations(buysoperations).
• SCOS =Supportcapacityofoperations,financialcapacityfor
t,i
operations(salesoperations).
• DGAP =Differencebetweenmaturityofinvestmentandma-
t,i
turityofliabilitiesfortheagentiattimet.
• EaR =Earningsatriskofagenti,attimetthatcanbeapplied
t,i
inearnings,Ebit,Ebitda,CashFloworCapital.
• CFaR =Cashflowatriskofagenti,attimet.
t,i
• EBITaR =Operatingincomeatriskofagenti,attimet.
t,i
• Dem =Demandlevelforeachagent.
t,i4.4. Modelformeasuringsystemicriskforenergyagents: General
87
processandphysicalprocessusingacomplexaproximation
• CC =Chargeforconfiability.
t
• CG =Cost ofgenerationfor eachagentthat hasdecapability
t,i
ofgenerateenergyusingdifferentsources.
• TD =TotalDemandinthesystem,foroneperiodoftime. (The
t
resultsarereachedusingadatabaseforonespecificyear).
The objective of the agents is to make transactions in the market
in order to reach the best profitability as they can, under the uncer-
tainty conditions, specifically financial conditions from others. Gen-
erally regulator guarantees these kinds of situations, but, thanks to
the inclusion of general measures of systemic risk like this research
proposal, each agent can take a look to the financial situation from
others.
FIGURE 4.6: Different levels for acting at the stock
market
Source:MedinaandMoreno,2007
Thelevelofdemandforeachagentcanbeless(shortage)orhigher
(surplus) than the energy contracts that are signed. If the contracts
arehigherthandemandlevel,thesurpluswillsellinstockexchange.
Therepresentationofthesituationisshowninthefigurenumber4.6.
And if the contracts are less than demand level, the shortage will be
boughtinstockexchange.
t
(cid:88)
Ee = EE (4.14)
n,i
n=1
t
(cid:88)
He = HE (4.15)
n,i
n=1
Inthescenariowheretheagentreachesitspointofmarginalequi-
librium, it means where price of sell is equal to the cost c = p the
t,i t,i
financial equilibrium is not achieved because it is necessary pay the
associated debt interest. In other words the operative equilibrium is
not enough for ensure the continuity of the company in the market,Chapter4. ModelingElectricityMarketsfromacorporate
88
perspective
becausethenextexpositionisadowngrade(riskqualification)when
thecapacityforhonoringtheobligationsarecompromised.
Thus strategies for the agent i at time t, can be defined below ac-
cording to their expected returns Roce and net income expected.
t,i
There are two kinds of agents under this evaluation, first the traders
and second the generators. Generally the objective is the same and
the financial model of business too, but the principal difference is in
the cost of generation because the trader does not generate electric-
ity. Is common that one company combines the business between
commercializationandgenerationofpower.
4.4.1 Agents Profit
Each agent evaluates the decision process, considering variables in-
volved in the physical phenomenon, in order to improve the per-
formance in the market. The risk perception and the value gener-
ation depend on preferences, outcomes (decision to buy or sell en-
ergy to/from other agent after risk evaluation) and the penalties or
awards inside of the framework of the decision (Bristow, Fang, and
Hipel,2014). Theprocessareshowninthefigure4.7.
FIGURE 4.7: Proposed agent-based model for model-
ingbehavior
Source:Computationsbyauthor-Bristow,Fang,andHipel,2014
Then,thedescriptionofthephysicalprocessstartwiththemulti-
plicationbetweentheamountofenergysoldincontracts,andenergy
prices contracted, with different buyers becomes in the operative in-
come. After,theproductbetweenenergypurchasedincontractsand
the different costs from sellers will be the cost of sales. Income and
cost of sales are the most important parts related to the construction
of state of incomes and losses, which describes the physical process.
Moreover the operative and management expenses, the quantity of4.4. Modelformeasuringsystemicriskforenergyagents: General
89
processandphysicalprocessusingacomplexaproximation
surplus energy and the quantity of shortages that will be traded in
thestockexchangeconsideringthespotprice.
Intheprocess,isnecessarytoincludeotherobligationsdemanded
by the operator or by the market itself. Those are for example, the
capital capacity and the forced savings that works as a contribution
to the stability of the system or to the taxes necessity from govern-
ment.
Earnings from operations generated in the purchase and sale of
energylistedabove,mustalsorecognizetheinterestexpensethrough
the debt. It means financial equilibrium (Toro, 2004). In the financial
frame, the earnings are called EBIT (Earnings before taxes depreci-
ation and amortization) or in other words operating income, which
dependsonbusinesscoreandinthecaseofelectricitymarketagents,
thepowertransactions.
4.4.2 Profitandlossesstatement: Representationofthe
physical financial process for traders
Theincomestateoftheagentinthemarketisdefinedasfollows:
n
(cid:88)
U = (S ×p −Q ×c )+(He −Ee )×pb −OyM −D ×Kd
t,i t,i,j t,i,j t,i,j t,i,j i i t t,i t,i t,i
i,j=1
(4.16)
Where,
• U =Netprofitforeachagent(inabsenceoftaxes).
t,i
• p =Thepriceattimetforcontracts.
t,i,j
• c =Costofenergyattimetforcontracts.
t,i,j
• Q =Quantityofenergypurchasedbyagentifromagentj.
t,i,j
• S =Quantityofenergysoldbyagentitoagentj.
t,i,j
• He =Quantityofenergysurplusbyagenti.
t,i
• Ee =Quantityofenergyshortagesbyagenti.
t,i
• pb =Spotriceofenergyinthestockexchange.
t
• OyM =Operativeandmanagementexpensesfromagenti.
t,i
• D =Totaldebtofagenti.
t,i
• kd =Interestrate,financialcostforagenti.
t,iChapter4. ModelingElectricityMarketsfromacorporate
90
perspective
The first part of the equation represents the quantity of energy
through contracts, because there are differences between purchases
(Q) and sold energy (S), which depends on the conditions signed
in each contract, time, dispatch, availability, and guarantees among
others.
The second part considers the quantity through stock electricity
market for reach the demand according to the shortage or also in or-
der to obtain a profit using the surplus. The operation in the market
suggest an intervention when the agents has or doesn’t has energy,
becausealltheenergyavailablemustbesoldorpurchasedgiventhat
itisimpossibletostore“thegoods"inwarehouses(Bohi,2013).
The third and last part of the equation is the consideration of the
operative expenses and the financial obligations related to interest.
That’swhytheoperatingequilibriumcannotbezero,becauseallthe
financialcapacitycomesfromtheoperationalbreakpoint(Ebit=0).
The consolidated expression defines the amount of money that
determines the global operation for each agent (trader or generator)
and is called "profit and losses statement", using a financial perspec-
tive. Then,theenergywillbeobtainedfromtheuseofownresources
(cash)andmoneythatcanbeobtainedthroughloansoreventheeq-
uity(capitalizationbyshareholders).
However, despite the fact that companies go through a thorough
andongoingevaluationinordertoensurethatnotcompromisedthe
financial system functionality, there are different variables and con-
straintsthatmustbeconsidered.
Thefollowingdefinitionisasimplificationofthenetprofit,elimi-
natingthefinancialexpensestheoretically(Damodaran,1996)(break-
point):
n
(cid:88)
Ebit = (S ×p −Q ×c )+(He −Ee )×pb −OyM
t,i t,i,j t,i,j t,i,j t,i,j i i t t,i
i,j=1
(4.17)
Then,forfulfillmentofthesalesinthemarket,tradersmustguar-
antee the disposition of risk, it means the value at risk associated to
thesales.
VaR1 = [(S +Dem −He )×(pz −p )]×2 (4.18)
t,i t,i t,i t,i t t,i
Adjustedapproximation,consideringthedefinitionsgivenbyCROM
"Capacidadderespaldodeoperacionesenelmercado"(energía,2012)
andadaptedtothedispositionofcapital. Thisfirstvalueatriskisthe
exposition of risk only when the agents are selling energy to others.
Thecoefficientnumber2istheenlargementoftheimpactinorderto
measure the VaR with 2 standard deviations; it means 95% of confi-
dence.4.4. Modelformeasuringsystemicriskforenergyagents: General
91
processandphysicalprocessusingacomplexaproximation
Where,
• Dem =Demandlevelforeachagent.
t,i
• pz =Scarcityprice(givenbytheoperatoraccordingtothemar-
t
ketconditions,inColombiaforexampletheexpositiontoNin´o
phenomenaandNin´aphenomena).
After the measure of the VaR1, considering the definitions given
by CROM (energía, 2012) with the respective adjustments, it is pos-
sible to establish the capital capacity from the perspective of sales.
The last sentence means that there are different mandatory condi-
tions when the trader is buying and when the trader is selling. Ac-
cordingtothis,thefollowingexpressionisthefinancialcapacity.
E −VaR1
t,i t,i
SCOS = (4.19)
t,i
(pz −p )×2
t t,i
Where,
• SCOS = Support capacity or financial capacity in order to re-
t,i
spondforsellagreements.
• E =Equityvalueofeachagent.
t,i
Then, there is another perspective from buys situation, because
eachagentmusthavedifferentfinancialcapacityaccordinghisposi-
tion in the transactions. That means, if one agent wants to buy en-
ergy, the regulator measures its leverage capacity in order to honor
the compromises because sometimes the payments are not in cash,
whichgeneratesaccountsreceivables.
Forfulfillthebuysinthemarket,tradersmustguaranteethedis-
positionofrisk,itmeansthevalueatriskassociatedtothebuys.
VaR2 = [(Q −Dem +Ee )×(p −pmin )]×2 (4.20)
t,i t,i t,i t,i t,i t
AdjustedapproximationconsideringthedefinitionsgivenbyCROM2
(energía,2012)andadaptedtothedispositionofcapital. Thissecond
valueatriskistheexpositionofriskonlywhentheagentsarebuying
energy to others. The coefficient number 2, again is the enlargement
oftheimpactinordertomeasuretheVaRwith2standarddeviations;
itmeans95%ofconfidence.
Where,
• pmin = minimal price (given by the operator) for recognitions
t
ofatleastthemanagementcostandthepublicnecessitiesCERE
(Impuesto sobre la renta para la equidad) and FAZNI (Fondo
de Apoyo Financiero para la Energización de las Zonas No In-
terconectadas)(Bogotáetal.,2011).Chapter4. ModelingElectricityMarketsfromacorporate
92
perspective
After the measure of the VaR2, considering the definitions given
byCROM(energía,2012),itispossibletoestablishagain,thecapital
capacityfromtheperspectiveofbuys. Thefollowingexpressioncon-
siders the mandatory conditions when the trader is buying energy,
in other words the financial capacity that comes from the financial
statementsandthepositioninthemarketmustbeguaranteed.
E −VaR2
t,i t,i
SCOB = (4.21)
t,i
(p −pmin )×2
t,i t
Where,
• SCOB = Support capacity or financial buys capacity to re-
t,i
spondtheagreements.
4.4.3 Constraints related to KRI
Constraints are established using the definitions given in the second
chapter about KRI and the maximum or minimum levels in some
cases in order to measure the total risk exposition. All the ratios and
calculations are founded in a specific interval of time, in this case is
possible to apply the calculations annually, monthly, daily or even
hourly.
Constrainsarethefollowing:
Coverratio
Firstconstrain,thecoverratiothatestablishesthecapacityofpaying
thefinancialobligationsassociatedtothedebt. Inotherwordsfinan-
cialriskanditmustbegreaterorequalto2.5accordingthedefinition
givenby(Tappeineretal.,2010)
Ebit
t,i
≥ 2.5 (4.22)
(D ×kd )
t,i t,i
Indebtedness
The second constrain is the level of indebtedness. This ratio is cal-
culated because is necessary find the maximum level of debt that
each agent can withstand before start a "default" process. The level
of maximum indebtedness depends on the generation of operating
income and the level must be less or equal to 4 according re results
givenby(Tappeineretal.,2010;Achleitneretal.,2011;Li,2015).
D
t,i
≤ 4.0 (4.23)
Ebit
t,i4.4. Modelformeasuringsystemicriskforenergyagents: General
93
processandphysicalprocessusingacomplexaproximation
Riskaversion
Thethirdconstrain,istheriskaversion,thelevelofgeneraltolerance
defined, but it depends on the risk aversion allowed by the operator
in order to ensure the fulfillment of the operations. There are 2 risk
measures, for sell (VaR1) and for buy (VaR2) energy, these VaR mea-
surements are provided by the Colombian market regulator, for this
reason only depend on the equity, operational and market compo-
nents. In all case, should be more flexible the agreements for sale
energy than agreements for buy. In the agreements for buying, the
levels of requirements are higher as it to acquire a contractual obli-
gation.
Therestrictionsexplainthetotalfinancialexposurethatshouldbe
less or equal to 10% of the equity for each agent in the case of sales,
and less or equal to 20% of equity in the case of buys following the
definitionsgivenby(Jorion,1996).
VaR1 ≤ 10%×E (4.24)
t,i t,i
VaR2 ≤ 20%×E (4.25)
t,i t,i
Financialleverage
Thefourthconstrainisrelatedtofinancialleverage. Therelationship
between debt and equity is called financial leverage, because is the
availabilityofcapitalforrespondingtofinancialdebtandthemixbe-
tween the capital sources (equity, debt) are the net assets. The ratio
must be less or equal to 80% according to (Kraus and Litzenberger,
1973)anditdependsonthebusinessmodel. Incommoditiescompa-
niesisusualtofindratiosover150%oreveninfinancialsector.
D
t,i
≤ 80% (4.26)
E
t,i
DurationGAP
Fifth constrain is "duration GAP". The result is the difference be-
tween maturity of investment and maturity of liabilities with finan-
cial cost, all of them in present value. If the "duration GAP" is high,
the company is exposed to an increase in the interest rate (market
risk)becausetheequityvaluewillbelessiftheratesgoup. Itmeans
it is possible immunize the balance sheet (Bierwag and Kaufman,
1985), for avoiding market risk when the duration GAP is small or
close to zero. The results given by [I’m] defined that DGAP can de-
creasetheriskexposure.
0 ≤ DGAP ≤ 1 (4.27)
t,iChapter4. ModelingElectricityMarketsfromacorporate
94
perspective
EaR-EBITaR
Thesixthconstraintaccordingtotheriskaversionofeachagent(com-
pany) and the calculation of the EaR and EBITaR depends on the
managementanditsstrategiesforthecontrolinfrontoftherisk(Va-
lencia,Jaramillo,andSAESP,2010). Thelimitcomesfromthecorpo-
rate perspective and the budget for the present period or the follow-
ing.
EaR ≤ 5%×U (4.28)
t,i t,i
EBITaR ≤ 15%×EBIT (4.29)
t,i t,i
Where, U and EBIT are defined for present period or could
t,i t,i
beaforecast.
Profitability
The seventh constrain is the best approximation to the return rate
in comparison with the cost of utilization of assets, from operational
perspective. The return of capital employed usually is estimated us-
ing the budget of the company and historical performance for next
periods. The return of capital employed must be greater than Wacc
in order to ensure the profitability of the company (Tirole, 2010). If
thein-equationissatisfied,thecompanyisintheprocessofgenerat-
ingvalueinthetime,withthechanceofimprovingthevalueforthe
nextperiods.
Roce > Wacc (4.30)
t,i t,i
Solvency
ThelastconstraintisproposedusingthebasefromBaselIII,formea-
suring the solvency in a company of financial services. This kind
of agents (companies) should have a solvency capacity according to
the international requirements (Repullo and Saurina Salas, 2011). It
means it can use Risk Weighted Assets RWA, proposing the risk of
each asset, and the most important assets in the case of market en-
ergyarethecontractsandthefixedassets.
E
t,i
> 8% (4.31)
Risk(Assets)
Where,theRisk(Assets)iscalculatedaccordingtotheexposition
of each asset, for example the transmission lines have a risk differ-
ent in comparison with the accounts receivable or intangible assets.
Theresultmustbegreaterthan8%accordingtodefinitionsgivenby4.5. Profitandlossesstatement: Representationofthephysical
95
financialprocessforproducers
(Repullo and Saurina Salas, 2011; Committee et al., 2010) and allow-
ing the existence of ability for responding to the obligations in the
mediumandlongterminthecaseofabankruptcy.
Therelationshipmodeledwillbethequantityofcontractsamong
the agents, or in cash (transactions) for explain the behavior of the
market or even is possible to consider the prices of buying or selling
undertherulesofthecontracts. Thefigurenumber4.8isarepresen-
tation of interactions where the red lines are sales and the blue lines
are buys in a market with 6 agents with the same business core. In
this case 6 agents can represent an important share of the total mar-
ketaccordingitssizeorthevolumeoftransactions.
FIGURE 4.8: Representationofinteractions
Source:Risker-Internalplatformdeveloped
4.5 Profit and losses statement: Representa-
tion of the physical financial process for
producers
Additionally to the trader’s income, the operating profit of the pro-
ducers will consider the cost of generation, and additional income
like a capacity charge. The new variables come from the Colombian
electricity markets and are referred to regulation and requirements.Chapter4. ModelingElectricityMarketsfromacorporate
96
perspective
Inabsenceoftaxesthefollowingequationdescribesthephysicalpro-
cess.
n
(cid:88)
U = (S ×p −Q ×c )+CC (He −Ee )×pb −CG −OyM −D ×Kd
t,i t,i,j t,i,j t,i,j t,i,j t,i i i t t,i t,i t,i t,i
i,j=1
(4.32)
Where,
• CC =Chargeforconfiability. Isaremunerationschemewhich
t,i
allows investment in power generation resources that are nec-
essary in order to ensure effectively the attention of energy de-
mandincriticalcondition,according(Rivieretal.,2000).
• CG = Cost of generation, is the cost associated to: the utiliza-
t,i
tionofgenerationsources,liketheuseofwater(hydroelectric),
coal (thermal), wind (Eolic) among others, and all the logistic
necessary in the generation process (central plants, machines,
turbines,reactors,dams).
Subjectedwiththesameconstraintsexposedinthelastsubsection
because the only change is the charge for confiability and the cost of
generation.
The regulator at the end of the period (year, month, day, hour)
must satisfy the totally of demand in the market, and guarantee the
dispatch at the beginning of the period related to interactions be-
tween the agents (transactions). Making good business under good
financialconditions.
(cid:88)
Dem = TD (4.33)
t,i t
Optimization
The method used for optimization in the proposed model, again is
the simplex method in order to find a utility maximization because
according to the equation, the behavior is linear. Under different
constraintsdescribedabove(constraintsrelatedtoKRI).
Inordertofindanoptimumpointistohaveequilibriumbetween
agents,withbestresponseinaccordancewithpurchasingandselling
process.
The vector of actions to be taken by each agent will be in two
ways, quantity of buys and quantity of sales, where Q and S repre-
i i
senteachaction.
The scenario simulation is performed for a year (the data base
comes annual) of operation programming, which requires the dis-
patchofenergytofinalconsumersthroughtraders,whoseresponsi-
bility is the fulfillment of each dispatch of energy. And other reason4.5. Profitandlossesstatement: Representationofthephysical
97
financialprocessforproducers
is the availability of financial information, because each agent esti-
mates its own financial situation for each mandatorily accounting
period, and they publish the results quarterly to "superintendencia
deserviciospúblicos"inColombia.
4.5.1 In Brief the model:
Fortraders,
n
(cid:88)
MaxU = (S ×p −Q ×c )+(He −Ee )×pb −OyM −D ×Kd
t,i t,i,j t,i,j t,i,j t,i,j i i t t,i t,i t,i
i,j=1
(4.34)
Andforproducers,
n
(cid:88)
MaxU = (S ×p −Q ×c )+CC +(He −Ee )×pb −CG −OyM −D ×Kd
t,i t,i,j t,i,j t,i,j t,i,j t,i i i t t,i t,i t,i t,i
i,j=1
(4.35)
Subjectto,
Ebit
t,i
≥ 2.5 (4.36)
(D ×kd )
t,i t,i
D
t,i
≤ 4.0 (4.37)
Ebit
t,i
VaR1 ≤ 10%×E (4.38)
t,i t,i
VaR2 ≤ 20%×E (4.39)
t,i t,i
D
t,i
≤ 80% (4.40)
E
t,i
0 ≤ DGAP ≤ 1 (4.41)
t,i
EaR ≤ 5%×U (4.42)
t,i t,i
EBITaR ≤ 15%×EBIT (4.43)
t,i t,i
Roce > Wacc (4.44)
t,i t,i
E
t,i
> 8% (4.45)
Risk(Assets)Chapter4. ModelingElectricityMarketsfromacorporate
98
perspective
Finally the demand must be realized through the aggregation of
differentindividualdemandsforeachagent.
(cid:88)
Dem = TD (4.46)
t,i t
The model is developed from a trader point of view, but it is
possible to consider the point of view of the generator agent’s with
changes in the equations like generation cost and charge for confia-
bility. The situation of traders is shown in the figure 4.9 considering
the definitions given by (Gnansounou et al., 2004). The agents take
all the strategies but the regulator is responsible of stability of the
market. Finally the model can be summarized in 4 steps, first of all
the inclusion of database with daily, monthly or annual periodicity.
Secondthecalculationsandtherunningofthemodelinordertofind
theresultstoimplementthethirdsteporsimulations. Finallytheop-
timizationcomesconsideringthemarketoutcomesandwiththeself
- learning the agents can take best strategies in next schedules of de-
mand.
FIGURE 4.9: Summarizedofthemodel
Source:ConsideringdefinitionsgivenbyGnansounouetal.,2004
The responsibilities of the regulator are control, reglamentation,
imposition of guarantees, restrictions, investor protection, controller
of price volatility, among others. In this sense, the society and the
securing of the dispatch of energy is the central goal of the regu-
lator that usually is a public entity. In the figure number 4.10, the
descriptions of the obligations of regulator and duties of the agents
are shown. Each agent, no matter the position as a trader, generator,
transmitter,orevencustomerhasdifferentpositionsinfrontofrisk.4.5. Profitandlossesstatement: Representationofthephysical
99
financialprocessforproducers
FIGURE 4.10: Dutiesandresponsabilities
Source:Computationsbyauthor
The description of physical phenomena through the equations
described above, can let understand how agents function from the
financialpointofview,concerningthetwomaincomponents,which
aretheinputsandoutputsofmoney. Insummary,incomestatement
that includes data from sales and cost needs to ensure operation.
In turn, the financial needs associated with debt are part of the re-
sourcestobetransferredtofinancialinstitutions.
The risk is concentrated in the inability to meet their obligations
with financial institutions and other agents with whom they have
made business. Therefore a thorough assessment of the situation of
the other agents is required as part of the process for the removal of
systemic risk, it means a risk that breaks system stability in a stag-
geredway.
Risk measures such as solvency, liquidity, DGAP, EaR, EBITaR,
indebtedness, coverage, leverage and others will be responsible for
controlling and managing risk behavior of companies. Thus, the ap-
plication of models that allow the integration of risk and determina-
tion of market equilibrium, become the main contribution of this re-
search. Howevertoproposeameasuretheequilibrium,thefirststep
was to understand the complexity arising from transactional system
bringingittomathematicalexpressions.101
Chapter 5
Results presentation,
comparison between
methodologies used and
explanation of financial risk
interface
5.1 General overview
Possessing measuring elements risks associated with new technolo-
gies, it is part of the actual current called financial innovation. Thus
in addition to using traditional systems in order to relate the agents
bymathematicalrepresentations,aplatformdeveloped"inhouse"is
used.
The platform’s main objective is the mathematical and strategic
representation of the advanced actions by agents from the perspec-
tive of financial risk. It is worth noting that the relationship pro-
cess between agents is done considering the mathematical exposed
inchapter4inparallelwiththerestrictionsfortheoperation.
Thanks to this, the analysts responsible for managing the risk
unit,theyhaveacomprehensivesystemthatwillfacilitatethedecision-
making process because it’s carried out under adaptive mechanism.
Thatis,theplatformincludestheimplementationofcomplexmodel,
and a number of components such as the risk limits represented in
colors for ease of interpretation. On the other hand the platform re-
sponds to the wish to make adjustments depending on the time in-
tervalandfinallysystemsize.
Subsequently, considering the database that was used, it will be
possibletomakesubstantiatedmeasuresbydifferentperiodsoftime,
consideringtheintensitydemandedbyanalystsandbymarket. Thus
the results can be displayed in hourly, daily, weekly, monthly, quar-
terly, semiannually or annually, depending on the information en-
tered. Even for purposes of strategic projection and planning of the
operation, may be considered financial statements estimations, de-
mandforecasting,priceprojectionamongothersinordertoconstructChapter5. Resultspresentation,comparisonbetween
102
methodologiesusedandexplanationoffinancialriskinterface
thetransactionalstageinthefuture.
For such purposes, it is essential to have additional tools in or-
der to improve results. These tools begin with the fundamentals in
financial planning that comes from enterprises valuation and corpo-
rate finance, associated with estimating the income statements and
profitability scenarios. Next, statistical models and those contem-
platingtheuseofnewtechnologiesassociatedwiththeestimationof
prices and demand levels, allow to project the size of the risk in the
futurefromtheapplicationcreated.
This chapter presents the results obtained based on the models
proposed in Chapter 4 and the methodologies used during the con-
duct of the investigation. First checking the unstable equilibrium
fromthefinancialpointofviewsubstantiatedonmodelingbasedon
gametheory,andtheinclusionofoptimization. Secondlythepresen-
tation of the complex model and calculation of equilibrium consid-
ering the interactions between agents in parallel with the respective
financialconstrains.
Finally, the comparison between the methodologies is made, un-
derlining the advantages for each one from the mathematical point
ofview,butalsothelimitationsthatinfluencethemodels.
Each result is obtained considering the information extracted an-
nuallyfromthebehavioroftheColombianelectricitymarket,butcan
replicate any transactional system where agents have a role. There-
fore,therelationshipbetweensuchagentsbecomesaninputvariable
todeterminethecomplexenvironment.
5.2 Database
TheacquisitionofDatabase,wasconsideringthetransactionsresults
fromColombianmarket,thepublicinformationsubmittedintheXM
webpageandthefinancialstatementsfromagents.
General data: the time frame of the study is assumed annually,
because the consolidated financial statements from traders have pe-
riodicity each year, discount rate considering market risk, interest
rate, transactions between traders (purchases, sales), energy prices
anddemandlevel. Inthetable5.1itspossibletoappreciateanexam-
pleoffinancialstatementforonetrader.
Electricitydemand: demandfortheannualframe(butthemodel
can stand intra-periods, yearly, monthly, weekly); in GWh and dis-
tributedinthedifferentagentsdependingonthedispositionandthe
numberofcontractssignedbyeachagent.
Transactions: the transfers between agents are dynamic and the
attributes of each transaction consider time, agreed price, quantity
and moment of dispatch. The agents can reprogram the operation
dependingonenergynecessities;andfinallyscheduledmaintenance
estimation.5.3. Resultsfromgametheorymodelation 103
IncomeStatement2015inmillionsCOP
OperatingIncome 1.608.855
(-)Costofsales 1.273.406
GROSSINCOME 322.502
GeneralExpenses 160.020
EBITDA 172.481
Depreciation-Amortization 93.372
OPERATINGINCOME(Ebit) 79.109
(+)OtherIncome 226.223
(-)OtherExpenses 81.936
INCOMEBEFORETAXES 214.697
(-)Taxes 73.012
NETINCOME 141.685
TABLE 5.1: IncomeStatementforatrader
Financial information comes from the agents. They must present
financial statements quarterly (balance sheet, profit and losses state-
ment and cash flow statement). Information is public but agents do
not calculate risk measures. Projections and forecast of accounts are
not an obligation, but in the medium term should be a recommen-
dation. In the table 5.2 we show the level of demand for the total
year2015intheColombianelectricitymarketforthemostimportant
agents.
Agent TotalDemandKhW Purchases Sales
CDSC 9.250.919.383 8.149.197.100 672.345.725
EDCC 12.273.803.176 11.254.686.825 603.281.250
EMIC 3.396.804.752 1.761.891.295 1.371.523.674
ENDC 3.320.754.704 3.320.754.704 10.975.883.102
EPMC 10.127.796.813 9.605.149.456 12.964.515.961
ISGC 2.019.005.226 3.962.225.096 11.466.354.764
TABLE5.2: Totaldemandandoperations: mostimpor-
tantagents2015
Discount rate and interest rate are different. The first is the ex-
position level of agents when liabilities and equity are considered.
Thesecondoneisthecostoffinancialobligationscontractedbyeach
agentwithfinancialinstitutionsorwiththefinancialmarket.
5.3 Results from game theory modelation
Theamountofequilibriumthateverytraderwilldemandforgetting
a market access, is determined by the best response to the strate-
gies that other traders establish. Thereby each agent of the marketChapter5. Resultspresentation,comparisonbetween
104
methodologiesusedandexplanationoffinancialriskinterface
startingfrominitialdemandlevels(atthebeginningoftheday),pro-
gramsitsownpurchasesinordertoreachthedemandsofthemarket
operatorandfulfillthetotaldemand. Itisimportanttoconsiderthat
the shortage of energy must be acquired through transactions with
their peers; to meet the requirements because of the asset (energy)
maynotbesubjecttoinventory.
Wemadeonethousandofsimulationsforthesystem,andweare
varying the demand function, which is assumed known, based on a
Poisson distribution, and it was explained in Chapter 4. Instability
of equilibrium is identified when the initial conditions are changed
given that under the same characteristics of the agents, only 32% of
the times, the demand is reached, sometimes we have exceeds and
manyothersthedemandisbelow.
In the Table 5.3 it can be identified the equilibrium, each trader
should get enough energy after acquiring shortages and selling sur-
pluses. The results using the game theory approximation, estimates
thedivergencebetweenthepracticalbehaviorandtheoreticalexpec-
tations. The results shown in the table are the average of the obser-
vationswhichreachedtheprogrammeddemand.
Such amount of energy will be delivered to meet global demand
intheproportionalimportance. Inotherwords,accordingtothesize
ofthetraderscomparedtogeneralmarket.
ThedeviationbetweenNashequilibriumandsimulateddemand
isachievedbecausenooneconsideredthefinancialabilityoftraders,
i.e. thefinancialrisk,that’swhythedeviationisveryhigh(forexam-
ple -98.6% in the first agent). However it can define that the system
isinequilibriumbecause:
• The global market demand is satisfied, i.e. fulfilling energy
needs in demand by consumers, is done, reaching the demand
planning
• Eachtradermaximizesitsprofitabilityusingthetransactionsin
the market. It means selling for more than the purchase price,
but demanding the maximum capacity that can be purchased,
withitsowncashflow
Financially,alltransactionsareaimedatmaximizingthevaluefor
the system, given that the total gain is the sum of the profits of the
commercializationagentsandtheprofitabilityofallpartiesinvolved
is ensured. However the equilibrium is unstable for two main rea-
sons, first, the time dependence and initial conditions, and second
by the non-inclusion of financial elements that limit transactions it
means financial capacity. For this reason the difference are so high
amongagents.
The second step consists of modeling maximizing system utili-
ties, to the optimal level of purchases, so the behavior of earnings is
asfollows. Inthefigure5.1ispossibletoidentifytheoptimizationof5.3. Resultsfromgametheorymodelation 105
ItemKwH Agent1 Agent2 Agent3 Agent4 Agent5
Database 2.535.978 3.461.280 4.247.833 1.058.474 6.544.004
Nash 34.515 54.661 977.747 3.282.095 1.737.096
Deviation -98.6% -98.4% -77.0% 210.1% -73.5%
ItemKwH Agent6 Agent7 Agent8 Agent9 Agent10
Database 1.463.392 1.580.555 13.369 417.749 2.322.658
Nash 4.629.105 1.182.221 4.092.605 6.733.847 5.661.230
Deviation 216.3% -25.2% 30512.2% 1511.9% 143.7%
ItemKwH Agent11 Agent12 Agent13 Agent14 Agent15
Database 5.420 3.603.312 3.226.897 510.115 343.589
Nash 4.957.669 3.372.603 1.885.519 4.116.855 1.802.120
Deviation 91369.9% -6.4% -41.6% 707.0% 424.5%
ItemKwH Agent16 Agent17 Agent18 Agent19 Agent20
Database 3.040.794 1.238.276 137.199 1.865.075 6.683.922
Nash 2.311.517 6.583.522 6.398.759 5.744.196 6.691.911
Deviation -24.0% 431.7% 4563.9% 208.0% 0.1%
ItemKwH Agent21 Agent22 Agent23 Agent24 Agent25
Database 499.439 1.058.540 2.175.504 1.367.756 153.610
Nash 1.297.058 3.743.266 4.533.851 6.600.712 4.800.809
Deviation 159.7% 253.6% 108.4% 382.6% 3025.3%
ItemKwH Agent26 Agent27 Agent28 Agent29 Agent30
Database 119.679 8.746 7.227.736 18.494 2.252.453
Nash 2.816.293 5.349.989 5.910.638 4.341.300 619.295
Deviation 2253% 61072% -18% 23374% -73%
TABLE 5.3: ResultsDatabaseVs. NashEquilibriumChapter5. Resultspresentation,comparisonbetween
106
methodologiesusedandexplanationoffinancialriskinterface
FIGURE 5.1: Utilityoptimization
Source:Computationsbyauthor
profits for all the system. Is important emphasize that for 30 agents
in this case the optimization of the utility is reached by simulation
process.
Provetheequilibriumfromafinancialpointofviewistodemon-
strate that there are a series of conditions for transactions of buying
andsellingenergy. Fromelsewheretheconditionsmustbeachieved
in order that all the agents will be financially agree, in terms of prof-
itability and facility of the implementation of its operations in the
market (Krause et al., 2006). However the equilibrium is unstable
by the concept of it and the assumptions underlying the game the-
ory, particularly the Nash equilibrium, which are (Heusinger, 2009;
Axtell,1999):
• Eachplayer’spredictedstrategyisthebestresponsetothepre-
dicted strategies of other players. No incentive to deviate uni-
laterally. Strategicallystable,orevenself-enforcing.
Withtheabove,itcanbesaidthatthesystemisinunstablefinan-
cialequilibriumbecause(ButtlerandAkchurina,2013):
• Does not consider transaction costs and the analysis are done
in the light of the hypothesis of efficient markets, where each
individual game includes the knowledge of the competitors in
depth.
The results differ from the simulated levels of demand consider-
ing historical data, and these quantities are quite significantly. The
deviation means that, to achieve the maximization of profits (Alos-
Ferrer and Ania, 2003), the system does not consider the financial
capacity (capital strength) to meet its obligations in the market. We5.3. Resultsfromgametheorymodelation 107
areassumingadifferentiatorelementtowriteanewequationthatin-
cludesrestrictionsonfinancialcapacity. Fortheequilibriumreached,
considering game theory is not necessary the inclusion of financial
conditions because the characteristics of the agents are quiet similar,
however it is possible to specialize the analysis with the inclusion of
moreelements,likecomplexityandfinancialconstraints.
FIGURE 5.2: Resultsfor30agents
Source:Computationsbyauthor
It does not set the difficulties that it may face the system if one
participant enters a possibility of financial default. Which would
generate a chain reaction that affects the financial stability of the op-
erationi.e. inefficiencyofthemarket.
The rescheduling of the consumption needs require the calcula-
tion of equilibrium, in other words the equilibrium is static for a pe-
riod of programming and the problem should be the revision of the
dispatch.
The figure 5.2 shows the evolution for 30 traders and the level
of energy demand in order to reach the Nash equilibrium. The solid
linepresentsthelevelsofdemandinequilibriumtooptimizetheutil-
ity, while the dotted line shows the simulated demand levels from
historicaldata.
In this work, the impact of risk indicators (key risk indicators)
KRI like a solvency, liquidity, earnings at risk, duration GAP, among
others,isnotcontemplated. Andtheimpactitdoesnotconsider,be-
cause the integration of the system is given by the volume of trans-
actions between agents, under the premise of reaching the demand
andbetterresponsefortheactionsofbuyingandsellingenergy.
On the other hand the financial ability of each participant is not
decisive to secure the equilibrium of the system. This, given that theChapter5. Resultspresentation,comparisonbetween
108
methodologiesusedandexplanationoffinancialriskinterface
FIGURE 5.3: Resultsfor20agents
Source:Computationsbyauthor
most important is the maximization of profits and under no circum-
stances, will consider the financial capacity by each agent to enter
in the market in order to buy or sell energy (Tushar et al., 2013).
The foregoing, under the assumptions of game theory because the
methodology considers knowledge of the competitor in-depth, and
this last consideration turns out to be quite ambiguous in this initial
approach.
FIGURE 5.4: Resultsfor10agents
Source:Computationsbyauthor
In this exercise, has been considered in parallel, the application
of the equilibrium to 20, 10 and 5 randomly traders agents. It found5.3. Resultsfromgametheorymodelation 109
similarly,animportantdivergencethatsupportstheconclusionoffi-
nancial instability. These results affirmed that the knowledge of the
financial situation of the other participants is insufficient and game
theoryproposesadeepknowledgefromothers. Subsequently,thefi-
nanciallevelknowledgefromtheotheragentssometimesisaffected
because the information presented is not so comprehensive and has
gapsbetweenperiods.
Thus,totheextentthattheagentsareless,theprobabilitytohave
at least one balance that converges with the historical situation (an
agent at equilibrium) decreases drastically. In the figure 5.3, fig-
ure 5.4 and figure 5.5 is possible to evidence that conclusion. It can
prove that decisions from equilibrium are quite different in compar-
ison of decisions from historical behavior. The results of the figures
5.25.35.45.5showthatifwehavealargernumberofagentsitispossi-
bletoreachatleastonevaluethatapproximatesthehistoricalvalue.
Ontheotherhandifagentsarefew,theresultdiffersfromthehistor-
icalvalue. Themodelconvergesmoreifwehavemoreagents.
FIGURE 5.5: Resultsfor5agents
Source:Computationsbyauthor
Financial default can be understood as the inability to account
for its obligations to creditors (Whited and Wu, 2006). In this vein
if traders, according to their relative importance, present an event
of this type; could generate a domino effect that would affect the
stabilityofthesystematall(Dobsonetal.,2007).
Incaseofdefault,theoperatorisnotresponsiblefortheeconomic
situationfacedbytraders,andthereforecannotvouchfortheirfinan-
cial numbers. In turn, the pending transactions the agent that is in
financialdifficulties(probabilityofdefault)shouldbecoveredbyan-
otherparticipantinordertorespondwiththeprogrammeddemand,Chapter5. Resultspresentation,comparisonbetween
110
methodologiesusedandexplanationoffinancialriskinterface
causing the operator will act as the central chamber of counterparty
risk,indirectly.
5.4 Complex systems Results
Followingwiththesecondmodelimplemented,aftertheresultsfounded
using game theory, the results using complex systems was consid-
ered. In the first model, all the assumptions and the program was
developed in MatLab (A) but in the second stage, a web application
wasbuiltinordertopresenttheresultsandtheanalysiswithaprac-
ticeway. however,beforetheimplementationoftheplatform,itwas
used one software open source called JULIA (B) in order to imple-
menttheoptimizationforonespecificperiod.
We named the platform "RisKer" because the objective of the re-
search is to propose a methodology integrated which allows the fi-
nancial innovation way, for risk measures. According to this, the
consideration of the equations, constrains, assumptions and the en-
tire model described in chapter 4, was modeled using the platform
andtheresultsareshowninaninterfaceforeachagent.
5.4.1 Implementation of RisKer platform
We implemented a web platform in order to wrap up the aforemen-
tioned core model. The main objective is to provide financial risk
management as a service for regulator entities as well as for energy
agentsinordertocontrolsystemicrisk.
The production architecture consists into a web server (Nginx)
with redundancy using an independent virtual server for each in-
stance. Thereisoneindependentdatabaseserver(MySQL),whichis
deployedwithredundancyaswell.
TheAgentDetailssectionpresentsfourtabswhichdisplayinfor-
mation about: Model forecast, buy and sell amounts, agent interac-
tions with other agents, stock information and Key Risk Indicators
(KRI)profile.
A practical platform implementation based on a complex sys-
temmodeltoprovideriskmanagementandmarketforecastsrelated
to energy trading agents is proposed. We implemented a proof-of-
concept service platform that provides financial risk indicators as-
sessmentaswellasrecommendationsformarketperformance.
Itproposesasfutureswork,theadditionofdifferentoptimization
models in order to benchmark multiple approaches. The platform
will evolve towards an automated system to generate triggers and
alarms regarding pre-defined contexts. We consider that automatic
data collection and data reporting are key elements to develop and
reinforce. Data mining and open data can be also linked to provide5.4. ComplexsystemsResults 111
useful information in order to increase model robustness and diver-
sity.
Regarding the proposed model, we consider the inclusion of op-
erational exposition variables like climatic variations, availability of
energy generators, terrorism attacks, regulation reviews, financial
hedges,andinternationaleconomicperspectives.
This can provide additional patterns and trends in order to pro-
videmoreaccurateanddetailedriskmanagement. Thebreakthrough
that suggests this work, is the possibility of study directly the finan-
cial phenomenon implicit in the operations, and synchronizes with
operational and macroeconomic developments that result in more
robustmodelsforanalysis,i.e. comprehensive.
Thus, with an identification of interactions and impacts, we can
avoid affecting the system sustainability, managing a new branch of
financialinnovation,whichiscalledsystemicriskverydifferentfrom
conventionallyknownsystematicrisk.
The interface aims to represent the financial behavior of agents
from its strictly financial situation, however, the model has the abil-
ity to support the inclusion of more elements that nurture, such as
operational analysis, internal and external factors. The developed
wasconductedunderjavascriptprogrammingandisasflexibleasa
web platform that uses a web service as it was described above. We
showntheconstructionofRiskerintheAppendixC
5.4.2 Agent’s description
There are several ways to represent the interactions between partic-
ipants in a system or a general market. In general terms the various
information exchanges that occur between agents channeled creat-
inginteractions(Tesfatsion,2003). Thusbusinessescontracted,trade,
business units, joint ventures, alliances, and generally every action
involving the flow of data can be transformed into interaction at
somepointoftime.
That said, the numbers related to energy contracts, become the
best representation of the interactions. Each agent that has business
with similar peers with the aim of achieving the required levels of
demand becomes an element that interacts through electric current
flowsandthereforethecashflowsgenerated.
In that sense, when contracted energy flows are very high, inter-
actionswillbecrucialbecauseoftheamounts. Graphicallytheagent
havingmorevolumebusinesswiththeircounterpartsbecomesacrit-
ical point agent for purposes of systemic risk. This behavior can be
evidenced from the figure 5.6, where red arrows represent sales and
blue arrows represent the total purchases for one agent from others
andviceversa.
A critical agent is one on which fall the most flows (interactions)
andwhichallowsthebeginningofmanyinteractionstoo. TheymayChapter5. Resultspresentation,comparisonbetween
112
methodologiesusedandexplanationoffinancialriskinterface
FIGURE 5.6: Specificrelationships
Source:XM-Risker:Internalplatformdeveloped
exist in the case of electricity, critical agents for purchases and sales
depending on the position in the market, however the most repre-
sentative of this behavior is the fulfillment of the demand from all
involved in the process (Costa et al., 2007). Thus, these important
agents (critical agents) have higher responsibilities because one in-
convenient related to default or financial failure can generate stag-
gered fail that generates systemic risk to business and the sustain-
abilityofthemarket.
Asitwasmentioned,inthefigure5.6itispossibletoseetheinter-
action of a selected randomly agent with 5 peers, from the financial
point of view and it provides businesses contracted. This graphical
representation, collected from a randomly chosen agent, considers
theamountofinformationexchange,whicharebecominglargerand
largerdependingonthemarketconditions,andthereforecanexpose
thestabilityofthesystematpresentandsubsequentperiods.
Agents have hired the demand at the beginning of the period,
therefore they must respond in some cases through purchases from
other agents. This level of demand is shown in figure 5.7 where ev-
eryoneestablishesenergyneedsforoperation.
The interactions for their part are detailed in figure 5.8 where is
established the amount of purchases and sales with each agent and
among them. In addition to the price at which such amounts are
contracted,whichvaryfromagenttoagentaccordingtheconditions
of contracts (this information is simulated because is confidential)
and alsoconsiders the historical behavior ofthe investor, andfinally5.4. ComplexsystemsResults 113
FIGURE 5.7: Agentsanddemandchart
Source:XM-Risker:Internalplatformdeveloped
itsempiricalriskevaluation.
FIGURE 5.8: Agent’s interactions and contracted
prices
Source:XM-Risker:Internalplatformdeveloped
On the other hand the specific overview for each agent, allows
having a generalized average risk for different participants. The fig-
urenumber5.9showstheriskforeachagentandinthefigure5.10is
establishedtheriskscorefromtheresultsofindicatorsaftercomput-
ing.
ThecolorsareassignedthankstothethresholdsdescribedinChap-
ter 3 related to KRI and classified from the results presented by (Ka-
plan,1997;Beasley,Branson,andHancock,2010;Scandizzo,2005).
Table5.4showsthecolorsaccordingtothethresholds"Stopligths",
usingtheinformationofaparticularagent,andcreatingresultsbased
on historical information. An agent with a high market share, can
concentrateacriticalpointifatthesametimereceivesanddistributes
energy flows in important quantities, given that expands the degree
ofrepresentativeness(Beasley,Branson,andHancock,2010).Chapter5. Resultspresentation,comparisonbetween
114
methodologiesusedandexplanationoffinancialriskinterface
Ratio Red Yellow
Coverage <2.0 ≥2.0and≤2.5
Leverage >5.0 >4.5and≤5.0
VaR1(Equity) >70% >60%and≤70%
VaR1(Equity) >70% >60%and≤70%
SCOB(Equity) >30% >20%and≤30%
SCOS(Equity) >30% >20%and≤30%
FinLeverage >80% >70%and≤80%
DGAP >5 >3and≤5
EaR(Equity) >10% >7%and≤10%
EBITaR(Equity) >10% >7%and≤10%
RoCe Roce<Wacc -
Wacc >20% >15%and≤20%
Solvency <1.0 ≥1.0and≤2.0
Liquidity <1.0 ≥1.0and≤2.0
Ratio Blue Green
Coverage ≥2.5and≤3.0 >3.0
Leverage ≥4.0and≤4.5 <4.0
VaR1(Equity) ≥60%and≤50% <50%
VaR1(Equity) ≥60%and≤50% <50%
SCOB(Equity) ≥10%and≤20% <10%
SCOS(Equity) ≥10%and≤20% <10%
FinLeverage ≥50%and≤70% <50%
DGAP ≥2and≤3 <2
EaR(Equity) ≥5%and≤7% <5%
EBITaR(Equity) ≥5%and≤7% <5%
RoCe Roce=Wacc Roce>Wacc
Wacc ≥10%and≤15% <10%
Solvency >2.0and≤3.0 >3.0
Liquidity >2.0and≤3.0 >3.0
TABLE 5.4: ThresholdsforKRI5.4. ComplexsystemsResults 115
FIGURE 5.9: XM-Riskprofileforonerandomagent
Source:Risker-Internalplatformdeveloped
FIGURE 5.10: Riskscorecalculatedfromindicators
Source:Risker-Internalplatformdeveloped
Similarly, label "General Overview" for comprehensive market,
is calculated from the level of relative importance of each agent for
transactions and is shown in the figure 5.11. That is, each agent is
responsible for a given level of demand and therefore increases its
responsibilityintermsoftheenergythattheyhavecommitted.
In the figure 5.12 it is possible to observe the level of relative
importance of each agent to represent the market, being EDCC the
largestsharewith30.39%ofthemarketdemand.
Interactions meanwhile, are displayed in figure 5.13 where for a
particular agent the purchases and sales levels are displayed based
on historical information from the database. In turn, the size of the
arrows determines the volume of contracted energy, whereby a crit-
ical point to the agent is generated when performing actions seller.
The point refers to the impossibility of advancing energy sales pro-
cesses with the counterparty without performing a rigorous risk as-
sessment(redarrows).Chapter5. Resultspresentation,comparisonbetween
116
methodologiesusedandexplanationoffinancialriskinterface
FIGURE 5.11: Generaloverviewandgeneralriskposi-
tionofthemarket
Source:Risker-Internalplatformdeveloped
Thus,assessthefinancialriskwiththeagentsforwhichenergyis
dispatchedthroughsales,itisanecessaryprocessbecausetheremay
bepossibilitiesofnon-paymentsinthefuture. Thisfailurecancreate
therefore a domino effect failure that will result in the inattention of
energy dispatch (Sioshansi, 2002), because financial flows can be in-
terrupted,andthoseflowsarenecessaryforthebusinessoperations.
The figure 5.14 shows interactions between all participants, rep-
resented in purchases and sales of energy to the market that con-
siders the interaction of 6 agents (red lines are sales and blue lines
arepurchases). AgentswhomademorepurchasesareEDCC,EPMC
and CDSC while sellers are ISGC, EMIC and ENDC. Graphically it
is possible to establish the concentration of systemic risk to identify
thoseagentsthatarecriticalpoints.
A failure in the critical points can compromise the entire system
ifariskeventoccurs,throughthecontagioneffect. Thereforetherel-
ative importance of each agent against the whole system is a very
relevant variable, it means if the agents ENDC, EPMC and ISGC
have problems with their counterparts, 93% of sales transactions are
threatened.5.4. ComplexsystemsResults 117
FIGURE 5.12: Relativeimportance
Source:XM-Risker:Internalplatformdeveloped
5.4.3 Optimization
To optimize the financial model, it is necessary express the KRI de-
pending on the target variable, which is the usefulness of each of
the agents and utility of the whole system. Thus the results using
thesimplexmethodreachitsmaximumvaluewithintherestrictions
definedfromtheKRIproposedinChapter3.
In order to describe de optimization process, the following in-
equalitiesarepresentedinquantityonsalesfunction.
2.5×D ×Kd +(Q ×c )−(He −Ee )×pb +OyM
t,i t,i t,i,j t,i,j i i t t,i
S ≥
t,i,j
p
t,i,j
(5.1)
(Q ×c )−(He −Ee )×pb +OyM + Dt,i
S ≥ t,i,j t,i,j i i t t,i 4.0 (5.2)
t,i,j
p
t,i,j
Wacc ×E +(Q ×c )−(He −Ee )×pb +OyM
t,i t,i t,i,j t,i,j i i t t,i
S >
t,i,j
p
t,i,j
(5.3)
D ≤ 80%×E (5.4)
t,i t,i
The value that throws the implementation of the algorithm is the
amount of energy that must be sold, considering the financial con-
ditions of the agents with which business are conducted. That value
hasasmainobjectivetoestablishhowbusinessshouldbedonewith-
outcompromisingfinancialmarketstability. Figure5.15summarizes
the results from the database in contrast to the results given by the
modelofsystemicrisk.Chapter5. Resultspresentation,comparisonbetween
118
methodologiesusedandexplanationoffinancialriskinterface
FIGURE 5.13: Interactions
Source:XM-Risker:Internalplatformdeveloped
Thus, the graph of interaction between agents evolves as follows
proposing a more equitable distribution of risk considering the op-
timizing profits. It may notice from the figure 5.16 that the arrows
sizes are more uniform because they propose a more equitable way
ofdoingbusinessamongparticipants. Withtheabove,themainpur-
pose is to maintain the financial balance of the system to make it a
financiallystable,itmeansinequilibrium.
5.4.4 Risk Situation
Regarding the situation of the financial risk of the agents, from the
figure 5.17 the level of coverage is determined for each of them in
comparison to their similar peers. All agents must have an indicator
above 2.5x (the constraint was proposed in Chapter 3), nevertheless
EMIC and EPMC agents would have a level of 1.77x and 0.58x re-
spectively,revealingthematerializationofafinancialrisk,that’swhy
other participants should review their business with these two com-
panies. The weighted average market for coverage located in 5.15x
demonstrating that there is no financial risk considering an isolated
scenarioforcoverageratio.
Theleveloffinancialleverageitselfrevealsthesameresultssince
the indicator is at 7.47x and 23.11x for the same pair of companies
(EMIC and EPMC) that confirms the recommendation of the review
all business having with these participants. The figure 5.18 sets the
level of leverage of each of the agents. Thus, the weighted average5.4. ComplexsystemsResults 119
FIGURE 5.14: Graphic representation: All market in-
teractions
Source:XM-Risker:Internalplatformdeveloped
market leverage is close to 7.9x and it means the market, as a whole
it’s possible to have a financial risk from leverage, because the indi-
catorshouldbelessorequalthan4.0x.
On the other hand return on capital employed (ROCE), in con-
trast to the weighted average cost of capital (WACC) can be seen
in the figure 5.19. In this case, companies or agents that generate
value are CDSC, EDCC, ENDC and ISGC given that their returns
outweigh their costs. Other agents are going through a process of
financial nonconformity given that over time can approach the de-
terioration of their financial statements. On weighted average the
market has a value of 12.7% and it means that generally the market
is profitable, additional reason for proposing a new scheme that al-
lows make more efficient business with the presence of agents like
EMICandEPMC(nonprofitableandunstablefinancially).
Finally, the risk concerning to exposure to changes in the interest
rate calculated through DGAP it is presented in figure 5.20. Given
that when the result is close to zero, there is less exposure, the agent
EMIChasminimalexposurecomparedtoitspeers. Whileingeneral
the market weighted average is close to 1.43x allowing define the
market does not have a risk representative exposure with respect to
interestrates,i.e. doesnotchangethemarketvalueofparticipantsin
fronttochangesintheinterestrateorinfronttheperceptionofrisk.Chapter5. Resultspresentation,comparisonbetween
120
methodologiesusedandexplanationoffinancialriskinterface
FIGURE 5.15: Risk comparison table, sales database
andsalesmodel
Source:Risker-Internalplatformdeveloped
FIGURE 5.16: Optimizinginteractions
Source:Risker-Internalplatformdeveloped
5.4.5 Comparison
This way, it can perform a comparison with the Nash equilibrium
found through game theory because is an unstable equilibrium in
viewofwhichdoesnotprovidefinancialinteractionsbetweenagents.
That is, the found equilibrium by modeling based on game theory
focuses on meeting the demand by setting the amount of energy
purchased in order to satisfy this demand without adding more re-
strictions than those associated with the market operation (demand,
amounts).
Instabilityofequilibriumingametheoryisidentifiedaswemen-
tioned in chapter 4 because when the initial conditions changed un-
der the same characteristics of the agents, the level of demand is not
reached. Equilibrium depends on the timing and don’t consider the
size of the agents because assumes is a Curnot situation with the
sameconditionsforalltheagents.
Therefore,thesecondresearchpartthroughmodelinginthecom-
plex environment interprets the results from financial combinations5.4. ComplexsystemsResults 121
FIGURE 5.17: Agent’sCoverage
Source:Computationsbyauthor-Risker
FIGURE 5.18: Agent’sLeverage
Source:Computationsbyauthor-Risker
and relationships between agents. However it is important to note
that the results are intended to ensure the supply of energy from a
position of financial equilibrium in a temporary moment. In other
wordstoperformtheexerciseinanotherperiod,itwillneedtolaunch
themodelagainandrunresults.
Finally if is required to make a programing for the next period,
incorporating forecast for different variables (financial statements,
demand, prices, contracts of energy, among others) will be an im-
portanttoolforfurthermodeling.
The great contribution of the proposed model is summarized in
identifyingtheamountofexposurethroughbusiness,thateachagent
can handle. It means, each agent must evaluate all the options and
strategiesinordertoimprovethefinancialresultsbutwithlessfinan-
cial risk exposition. It is important to remark that agents operate in
themiddleofthreeelementsasliquidity,riskandprofitability,which
mustmanagetroughusingofdifferenttoolsandRiskerplatformcan
beoneofthem.
In the table 5.5 it is possible to see the differences between theChapter5. Resultspresentation,comparisonbetween
122
methodologiesusedandexplanationoffinancialriskinterface
FIGURE 5.19: RoceVs. Wacc
Source:Computationsbyauthor-Risker
FIGURE 5.20: Agent’sDGAP
Source:Computationsbyauthor-Risker
results reached by game theory model and complex model. The de-
viationcouldbeunderstoodasaresultconsideringconstrainsinthe
second case. The deviation is less in some cases but it doesn’t mean
that results are fairly adjusted; at the end it depends on the financial
situationfromotheragents.
Item Agent1 Agent2 Agent3
DeviationNash 216.3% 30512.2% 4563.9%
DeviationComplexsystem 13466% n.a. -67%
Item Agent4 Agent5 Agent6
DeviationNash 108.4% -73% -77%
DeviationComplexsystem 10% -52% -3%
TABLE 5.5: Deviationscomparison.5.4. ComplexsystemsResults 123
General Conclusions
The current scenario that passed the electricity sector, not only the
Colombian even around the world, is the one to propose improve-
mentsandmeasuringdifferenttypesofexposures. Forexamplepower
generation in countries like France it is represented in nuclear 76%;
11%hydro;Conventionalthermal10%;3%othersources(Awerbuch,
2006). Thismakesthecountryisaminoruseroffossilfuels,andhav-
ingdiversesourcesofgeneration,thatcanbecomeareferenceforde-
veloping countries. In turn consumption in Colombia is about 15%
of what is consumed on French territory, but despite this there are
lessons that can be taken such as portfolio optimization and supply
flow amid stable financial conditions (Colombia It is environmen-
tally sustainable because 75% of the generation is hydro). Accord-
ingtothis,therelationshipbetweenefficiencyandsustainabilityisa
powerful mix that tries to ensure the operation of the system, that’s
why this proposals wanted to contribute even though we are focus-
inginoneelement,itmeansfinancialequilibrium.
TheenergymarketinColombiacantrademorethan30billionpe-
sos, which represents about 3.5% of GDP, in addition to maintaining
productiveresourcesofthecountryandaneventofapowerinatten-
tionthesupply,producehighcostsandfutureproblemsasinstability
of the market. From the results, it have started studies that has been
focusedonthe continuityofthenetwork, itmeansinphysicalassets
while for intangible issues such as financial tools, economic stability
and others, usually have been the traditional evaluation and clas-
sic measurement. . But the problem is not the manner of measure,
the different problems comes from the assumptions and the treat-
ment. In this thesis, we are justifying the necessity of new tools and
the liberalization not only from natural oligopolies or monopolies,
but rather the liberalization from traditional rules because the mar-
kethasconditionsthatevolve.
For this reason the consideration of different elements as those
proposed for example by Basel, such as the recognition of risk for
each component of assets and subsequent integration into different
schemesformeasuringrisk,isagoodadvance. Thisbecauseisafur-
ther step to the continuation of this research project, in other words,
inthefuturewillbepossibletocontemplateonemeasureoneweighted
average by risk level applied to the sources of power generation,
transmission networks, distribution and consumption, and thereby
calculateamorecriticalsolvency.
Havesystemsthatallowthemeasurementofriskoftheagentsin
the electricity markets from a corporate perspective, are a good step
forward in the management of organizations. At the same time theChapter5. Resultspresentation,comparisonbetween
124
methodologiesusedandexplanationoffinancialriskinterface
preoccupation for the stability of the operations from the financial
point of view, but with an economic impact on the management of a
countryorevenaregion. Allinordertoensuresustainabilityconsid-
ering the corporate risk measurements, which are passing through
the establishment of relations between the agents that trade energy,
in other words ensure compliance of the business transactions. Such
relationships in this research project were conducted in two stages
that are game theory and agent-based modeling with complex ele-
ments.
Gametheoryisamethodologythatissupportedonasimplecon-
ceptofinteractionbetweenparticipants. However,thismethodology
integratesacomplexmathinordertodeterminewhatisnotobvious,
itmeanstheequilibriumbetweentheparticipants. Nevertheless,be-
ing a very theoretical interpretation of physical phenomena in view
of which is based on very ambitious assumptions as efficiency and
knowledge of participants in depth could have problems in realistic
scenarios. Since not considered KRI (Key Risk Indicators) and the
financialcapacityofthetraders,then,theequilibriumisafinancially
unstable equilibrium, i.e. for academic purposes can be useful but
forpracticalpurposesisunrealistic. Itservestodescribethephysical
phenomena, of how agents interact but when considering variables
of financial and economic order does not respond to alerts that are
necessaryforpropermonitoringofoperations.
In the future, it is possible to consider different methodologies to
join the game theory and support the assumptions. It means inte-
grate for example complex situations for lift restrictions that exist in
the rules of game theory. Thus the results will be more adjusted to
thecomplexrealityofthemarket.
A system is complex if there are interactions between agents in-
volvedinaprocessandthattheseinteractionsusuallyareofdifficult
interpretation. Interactions they must also be accompanied by the
mathematical description of physical phenomena that support the
systems constraints. Therefore in the second stage we implemented
a model based on agents with complex elements that allows relate
all the components of a financial nature holistically. In turn, the in-
teractions can be translated for this thesis project in limitations for
the realization of efficient business. Thus the inclusion of KRI from
a perspective of integration within a complex model, describes the
operation of the system and the phenomenon that occurs through
transactions. It becomes an advance in view that most of the current
analyzes focus on indicators in isolation way, as the case of tradi-
tional financial analysis, however this project aims to integrate mea-
surementsfromitscomplexsituation.5.4. ComplexsystemsResults 125
Financially,oneofthemostimportantelementsisthataneventof
defaultoccurs,andifdefaultisnotpresentedthesystemisinequilib-
rium. It is possible to explore other measures to support the equilib-
rium but from different methodological approaches to game theory,
integrating the complexity and risk indicators such as solvency, liq-
uidity, earnings at risk, Ebit at risk, equity at risk, duration Gap and
debt management, looking indicators that will work for the system
providingearlywarnings.
Systemic risk is an innovative current that has been taking rel-
evance gradually in the academic and business discussions. Is the
risk of failure or in other words a series of events triggered or cas-
cade behavior, this risk spreads like a virus that infects other ele-
ments. Now, the contagion effect determines the behavior of the en-
tire system from a single element that disturbs everyone else. With
the results of this project and ranges from indicators, it is possible to
anticipatesystemicrisk,however,aspaceforresearchturnsouttobe
quantifying the effect of systemic risk, including by integrating the
existenceofoperationalrisks.
The construction of the "Risker" platform goes beyond the scope
ofthisresearchproject,howeverallresultscomefromtheimplemen-
tation of this software. In this sense, is proposed an interface for be
usedintheprocessofstrategicdecisionsthatcancontainanyamount
ofagentsinthefuturewiththeirrespectivemeasurementsandinter-
actions. Similarlyitremainspossibletoincludetoolsforforecasting,
such as neural networks, fuzzy inference systems, expert systems,
nonlinear systems, real options, among others. All this with the aim
to estimate as closely as possible, the behavior of the risks for ex-
posedcompanies.
Finally,thedevelopedmodelcanbeappliedtoanytypeofindus-
try, i.e. that can be replicated in different markets where relations
between agents occur. However it is necessary to understand which
aretheKRIthatcanbeappliedtothemarket,andofcourse,describe
in a practical way, the physical phenomenon that is in front of the
market.127
Appendix A
MatLab Code
n=30;%inputagents;
Ac=29;%inputstrategies
Es=input(’Scenario: ’);
dias=299;%inputNofdays;
dist=xlsread(’Tesis.xlsx’,2);%Demand
t=1;%timevector.
pconv=0;%from0(convergencepoint)
mij=xlsread(’Tesis.xlsx’,1);
%transfercostmatrix
k=0;
ep=0.0005;%epsilonvalue
fori=1:n
forj=1:n
k=k+1;
m(k)=mij(i,j);
end
end
%Chossescenario
ifEs==1%average
ci=213;
pi=215;
zi=26;
vi=ci;
elseifEs==2%max
ci=348;
pi=366;
zi=26;
vi=ci;
elseifEs==3%min
ci=138;
pi=165;
zi=26;
vi=ci;
elseEs==4%probable
ci=214;
pi=216;128 AppendixA. MatLabCode
zi=26;
vi=ci;
end
%startthevectorht (t,i)
1
ht =zeros(1,n);
1
%vectorA(differentactions).
fori=1:Ac
T(i)=i-1;%strategieschoosed
end
xo=randint(1,30,[5420,7227736]);%Demandinterval
fori=1:n
forj=1:length(T)
ifxo(i)==T(j)
Fo(i,j)=1;
else
Fo(i,j)=0;
end
end
end
BestStrategy
F=Fo;
norma=1;
whilet<=dias
t=t+1;
fori=1:n
temp=Fo;
temp(i,:)=[];
xe(i,:)=temp*T’;
end
fori=1:n
temp=dist;
temp(i)=[];
de(i,:)=temp;
end
fori=1:n
temp=ht ;
1
temp(i)=[];
ht e(i,:)=temp;
1
end
fori=1:n
forj=1:length(T)
ifxe(i,j)<=de(i,j)
se(i,j)=xe(i,j);AppendixA. MatLabCode 129
else
se(i,j)=de(i,j);
end
end
end
fori=1:n
forj=1:length(T)
ifxe(i,j)+ht e(i,j)<de(i,j)
1
ee(i,j)=de(i,j)-xe(i,j)-ht e(i,j);
1
else
ee(i,j)=0;
end
end
end
fori=1:n
forj=1:length(T)
ifxe(i,j)+ht e(i,j)>de(i,j)
1
he(i,j)=xe(i,j)+ht e(i,j)-de(i,j);
1
else
he(i,j)=0;
end
end
end
end
%BestAnswerfromCachon,consideringtheaverageofdemand
fori=1:n
x(i)=poissinv((pi-ci)/pi,sum(de(i,:)))
x(i)=(floor(dist(i))+sum(ee(i,:))) -ht (i)
1
ifx(i)>5420
x(i)=poissinv((pi-ci)/pi,sum(de(i,:)));
elseifx(i)<5420
x(i)=0;
end
end
Simultation
d=poissrnd(dist);
xt(t,:) =x;
fori=1:n
ifx(i)+ht (i)<=d(i)
1
s(i)=x(i)+ht (i);
1
else
s(i)=d(i);
end130 AppendixA. MatLabCode
end
%Surplusvector
fori=1:n
ifx(i)+ht (i)>d(i)
1
h(i)=x(i)+ht (i)-d(i);
1
else
h(i)=0;
end
end
%Shortagevector
fori=1:n
ifx(i)+ht (i)<d(i)
1
e(i)=d(i)-x(i)+ht (i);
1
else
e(i)=0;
end
end
k=0;
fori=1:n
forj=1:n
k=k+1;
ee(i,j)=ee(k);
end
end
%Maximizationofthefunction
U=pi*s-ci*x-zi*ht ;
1
Umed(t)=(sum(U))/t;
fori=1:n
u(t,i)=pi*s(i)-ci*x(i)-zi*ht (i)+sum(ee(i,:))*vi+((sum((pi-vi-mij(:,i)).*(ee(:,i)))));
1
umed(t,i)=(sum(u(:,i)))/t;
end
b=d’;
A=eye(n,n);
f=U;
lb=zeros(n,1);
options=optimset(’LargeScale’,’off’,’Simplex’,’on’);
[x,fval,exitflag]=linprog(f,A,b,[],[],lb,[],[],options)
ht =h-sum(ee’);%Surplus
1
plot(xo,’r’)
holdon
plot(x,’b’)
title(’NashEquilibruim’);
ylabel(’EnergyKwh’);AppendixA. MatLabCode 131
[o,l]=meshgrid(1:1:30);
v=diag(x);
surf(o,l,v)
holdon
r=diag(xo);
surf(o,l,r)
title(’NashEquilibruim’);
ylabel(’EnergyKwh’);
colorbar;
shadingflat133
Appendix B
Julia Code
julia>usingJuMP
julia>usingGLPKMathProgInterface
julia>sfLpModel=Model(solver=GLPKSolverLP())Feasibilityprob-
lemwith: *0linearconstraints*0variablesSolversettoGLPKMath-
ProgInterface.GLPKInterfaceLP.GLPK
julia>c=[170;109;146;147;146;134]
6-elementArrayInt64,1:
170109146147146134
julia>A=-[100000;
010000;
001000;
000100;
000010;
000001
]
6x6ArrayInt64,2:
-100000
0-10000
00-1000
000-100
0000-10
00000-1
julia>A=[
100000;
010000;
001000;
000100;
000010;
000001
]6x6ArrayInt64,2:
100000
010000
001000134 AppendixB. JuliaCode
000100
000010
000001
julia>b=[1402;3658;1795;5476;23235;5932]
6-elementArrayInt64,1:
1402
3658
1795
5476
23235
5932
julia>m,n=size(A)
julia>@defVar(sfLpModel,x[1:n]>=0)
6-elementArrayJuMP.Variable,1:x[1]
x[2]
x[3]
x[4]
x[5]
x[6]
julia>fori=1:m
@addConstraint(sfLpModel,sumA[i,j]*x[j],j=1:n>=b[i])
end
julia>@setObjective(sfLpModel,Max,sumc[j]*x[j],j=1:n)
170x[1]+109x[2]+146x[3]+147x[4]+146x[5]+134x[6]
julia>c=[1502;3744;2250;10056;27557;11327]
6-elementArrayInt64,1:
1502
3744
2250
10056
27557
11327
julia>fori=1:m
@addConstraint(sfLpModel,sumA[i,j]*x[j],j=1:n<=c[i])
end
julia>@setObjective(sfLpModel,Max,sumc[j]*x[j],j=1:n)
1502x[1]+3744x[2]+2250x[3]+10056x[4]+27557x[5]+11327x[6]135
Appendix C
Risker Construction
Therearetwoarchitecturemodels,testandproduction. Thefirsttest
platform uses one virtual server using Nginx as web server and in
thesameinstanceweuseMySQLasdatabaseprovider. Inthefigure
C.1wedepictthetestimplementationarchitecture.
FIGURE C.1: TestArchitecture
Source:Computationsbyauthor
Anadditionalfileserverisusedfordataandconfigurationsbackup.
ThelastdescriptionispresentedinthefigureC.2.
The platform is composed of a landing page that are shown in
thefigureC.3,followedbyaloginauthentication,whichleadstothe
maindashboardspaceaccordingtofigureC.4.
The main dashboard page provides three tabs. The first one pro-
vides the list of energy company agents (traders, generator or dis-
tributor as well). A short name is display with a full name display
while hovering. The agent display has two modes compact and ex-
panded. The compact model displays the short name and the total
energydemandassignedtothatagent. Theextendedmodeldisplays
the total energy for buy and sell as well as the current prices related
tocontractsbetweenagents. ItcanappreciateinfigureC.4andfigure
C.5thatcancollapsedandexpand.136 AppendixC. RiskerConstruction
FIGURE C.2: ProductionArchitecture
Source:Computationsbyauthor
FIGURE C.3: LandingPage
Source:Risker-Internalplatformdeveloped
The last panel displays a global overview of the whole system
with corresponding KRI’s. The metrics are colored regarding pre-
defined thresholds that will be explained after. The thresholds are
graded in four categories: red (critical), yellow (warning), blue (ac-
ceptable),green(good)(Beasley,Branson,andHancock,2010;Sioshansi,
2002).
The second main tab depicts each agent interaction with rest of
the system. We provide an interactive graph with proportional ar-
rows showing buy/sell relationships as well as total traded energy
amounts(figureC.6). Inthegeneralcasethemodelwasimplemented
for n agents, that’s way is it possible to see many arrows who repre-
sented the business size between agents. But in the second part of
theanalysis,asimulatedmarketisrepresentedwith6agents.AppendixC. RiskerConstruction 137
FIGURE C.4: PlatformDashboard
Source:Risker-Internalplatformdeveloped
FIGURE C.5: Collapsed/ExpandedAgent
Source:Risker-Internalplatformdeveloped
FIGURE C.6: AgentsInteractions
Source:Risker-Internalplatformdeveloped139
Bibliography
Achleitner, Ann-Kristin et al. (2011). “Structure and determinants of
financial covenants in leveraged buyouts”. In: Review of Finance,
rfq031.
Agarwal, Tarun and Shuguang Cui (2012). Noncooperative games for
autonomousconsumerloadbalancingoversmartgrid.Springer.
Aguilar, Argemiro and Javier Díaz (2004). Una visión al mercado eléc-
tricocolombiano.UnidaddePlaneaciónmineroenergética.
Alos-Ferrer, Carlos and Ana Ania (2003). “The Stock Market Game
andtheKellyNashEquilibrium”.In:DepartmentofEconomicsDis-
cussion Paper, University of Vienna, forthcoming in Journal of Mathe-
maticalEconomics.
Apt, Jay et al. (2004). “Electrical blackouts: A systemic problem”. In:
IssuesinScienceandTechnology20.4,pp.55–61.
Awerbuch,Shimon(2006).“Portfolio-basedelectricitygenerationplan-
ning:policyimplicationsforrenewablesandenergysecurity”.In:
Mitigation and adaptation strategies for Global Change 11.3, pp. 693–
710.
Axtell, Robert (1999). The emergence of firms in a population of agents:
local increasing returns, unstable Nash equilibria, and power law size
distributions.Citeseer.
Babic, Jurica (2014). Agent-based Modeling of Electricity Markets in a
SmartGridEnvironment.
Bak, Per and Kan Chen (1991). “Self-organized criticality”. In: Scien-
tificAmerican;(UnitedStates)264.1.
Bak, Per, Chao Tang, and Kurt Wiesenfeld (1988). “Self-organized
criticality”.In:PhysicalreviewA38.1,p.364.
Barreira Turnes, Ma T (1995). “El riesgo de interés y su impacto en
elmargenfinancierodelasentidadesdecrédito:unarevisióndel
modelo de" Gap de Duration"”. In: Análisis Financiero 66, Not–
availabe.
Basak,SuleymanandAlexanderShapiro(2001).“Value-at-risk-based
riskmanagement:optimalpoliciesandassetprices”.In:Reviewof
Financialstudies14.2,pp.371–405.
Batty, Michael (2007). Cities and complexity: understanding cities with
cellularautomata,agent-basedmodels,andfractals.TheMITpress.
Beasley, Mark S, Bruce C Branson, and Bonnie V Hancock (2010).
“Developingkeyriskindicatorstostrengthenenterpriseriskman-
agement”. In: ERM Initiative at North Carolina State University and
the Committee of Sponsoring Organizations of the Treadway Commis-
sion,Raleigh,NC.140 BIBLIOGRAPHY
Beatty, Anne, Krishnamoorthy Ramesh, and Joseph Weber (2002).
“Theimportanceofaccountingchangesindebtcontracts:thecost
of flexibility in covenant calculations”. In: Journal of Accounting
andEconomics33.2,pp.205–227.
Bierwag,GeraldOandGeorgeGKaufman(1985).“Durationgapfor
financial institutions”. In: Financial Analysts Journal 41.2, pp. 68–
71.
Boccara, Nino (2010). Modeling complex systems. Springer Science &
BusinessMedia.
Bogotá,CámaradeComerciodeetal.(2011).“Eficianciaenergéticay
energías limpias: Lineas de financiamiento para proyecto de efi-
cienciaenergéticayenergíaslimpias”.In:
Bohi, Douglas R (2013). Analyzing demand behavior: a study of energy
elasticities.Routledge.
Borenstein,Severin,JamesBushnell,andChristopherRKnittel(1999).
“Marketpowerinelectricitymarkets:beyondconcentrationmea-
sures”.In:TheEnergyJournal,pp.65–88.
Bouchaud, Jean-Philippe and Marc Potters (2003). Theory of financial
riskandderivativepricing:fromstatisticalphysicstoriskmanagement.
Cambridgeuniversitypress.
Bristow, Michele, Liping Fang, and Keith W Hipel (2014). “Agent-
based modeling of competitive and cooperative behavior under
conflict”.In:Systems,Man,andCybernetics:Systems,IEEETransac-
tionson44.7,pp.834–850.
Buehler,KevinSandGunnarPritsch(2003).“Runningwithrisk”.In:
McKinseyQuarterly4,pp.40–49.
Buriticá Chica, Yenny Marcela et al. (2014). “Indicadores de alerta
temprana del riesgo de crédito para el Mercado de Energía May-
oristaColombiano”.In:
Buttler, Jens and Natalia Akchurina (2013). “Nash equilibria in nor-
malgamesviaoptimizationmethods”.In:ControlConference(ECC),
2013European.IEEE,pp.724–729.
Cachon, G and S Netessine (2004). “Game theory in supply chain
analysis.HandbookofQuantitativeSupplyChainAnalysis:Mod-
eling in the eBusiness Era. edited by D. Simchi-Levi, S”. In: Wu
andZ.Shen.Kluwer.
Camerer,ColinF,Teck-HuaHo,etal.(2015).“BehavioralGameThe-
ory,ExperimentsandModeling”.In:HandbookofGameTheory4.
Chaffai, Mohamed and Michel Dietsch (2015). “Modelling and mea-
suringbusinessriskandtheresiliencyofretailbanks”.In:Journal
ofFinancialStability16,pp.173–182.
Chan, Kam Fong and Philip Gray (2006). “Using extreme value the-
ory to measure value-at-risk for daily electricity spot prices”. In:
InternationalJournalofForecasting22.2,pp.283–300.
Colombia, Constitución Política Constitución de (1991). “Constitu-
ciónpolíticadeColombia”.In:Bogotá,Colombia:Leyer.BIBLIOGRAPHY 141
Committee, Basel et al. (2010). “Basel III: A global regulatory frame-
work for more resilient banks and banking systems”. In: Basel
CommitteeonBankingSupervision,Basel.
Costa, L da F et al. (2007). “Characterization of complex networks:
Asurveyofmeasurements”.In:AdvancesinPhysics56.1,pp.167–
242.
CureVellojin,Lailaetal.(2009).“Juegoficticiopararesolverunjuego
de demanda dinámica en una cadena de abastecimiento de dos
nivelescontomadedecisiónenunnivel.”In:
Dahlgren,Robert,Chen-ChingLiu,andJacquesLawarree(2003).“Risk
assessmentinenergytrading”.In:IEEETransactionsonPowerSys-
tems18.2,pp.503–511.
Damodaran,Aswath(1996).Corporatefinance.Wiley.
Davies,Jonathanetal.(2006).“Keyriskindicators–theirroleinoper-
ationalriskmanagementandmeasurement”.In:ARMandRiskBusi-
nessInternational,Prague,pp.1–32.
Day, Christopher J, Benjamin F Hobbs, and Jong-Shi Pang (2002).
“Oligopolisticcompetitioninpowernetworks:aconjecturedsup-
ply function approach”. In: Power Systems, IEEE Transactions on
17.3,pp.597–607.
Dekel, Eddie, Marciano Siniscalchi, et al. (2014). “Epistemic game
theory”.In:HandbookofGameTheory4.
Denton, Michael et al. (2003). “Managing market risk in energy”. In:
PowerSystems,IEEETransactionson18.2,pp.494–502.
Dobson,Ianetal.(2007).“Complexsystemsanalysisofseriesofblack-
outs:Cascadingfailure,criticalpoints,andself-organization”.In:
Chaos:AnInterdisciplinaryJournalofNonlinearScience17.2,p.026103.
Domench,PabloArchel(2003).“Ladivulgacióndelainformaciónso-
cialymedioambientaldelagranempresaespañolaenelperíodo
1994–1998: situación actual y perspectivas”. In: Spanish Journal of
Finance and Accounting/Revista Española de Financiación y Contabil-
idad32.117,pp.571–601.
energía, Ministerio de Minas y (2012). Resolución 156 de 2012: Defini-
cióndelacapacidadderespaldodeoperacionesenelmercadodeenergía
eléctrica.RepúblicadeColombia.
Erb,ClaudeB,CampbellRHarvey,andTadasEViskanta(1996).“Po-
litical risk, economic risk, and financial risk”. In: Financial Ana-
lystsJournal52.6,pp.29–46.
Fischer, Thomas and Jesper Riedler (2014). “Prices, debt and market
structure in an agent-based model of the financial market”. In:
JournalofEconomicDynamicsandControl48,pp.95–120.
Gatti, Nicola, Marco Rocco, and Tuomas Sandholm (2013). “Algo-
rithmsforStrongNashEquilibriumwithMorethanTwoAgents.”
In:AAAI.
Gibbons,RobertS(1997).Anintroductiontoapplicablegametheory.142 BIBLIOGRAPHY
Gnansounou,Edgardetal.(2004).“Marketorientedplanningofpower
generation expansion using agent-based model”. In: Power Sys-
tems Conference and Exposition, 2004. IEEE PES. IEEE, pp. 1306–
1311.
Gómez-Bezares,Fernando(2010).“Novedadesenlasfinanzascorpo-
rativas”.In:Boletíndeestudioseconómicos65.199,p.5.
Greenspan,Alan(2007).“Theageofturbulence:adventuresinanew
world”.In:FinanceandDevelopment-EnglishEdition44.4,p.49.
Hertz,DavidBendelandHowardThomas(1983).Riskanalysisandits
applications.WileyChichesteretc.
Heusinger,Annavon(2009).“Numericalmethodsforthesolutionof
the generalized Nash equilibrium problem”. PhD thesis. Kyoto
University.
Hughes,JohnS,DennisELogue,andRichardJamesSweeney(1975).
“Corporateinternationaldiversificationandmarketassignedmea-
suresofriskanddiversification”.In:JournalofFinancialandQuan-
titativeAnalysis10.04,pp.627–637.
Humphrey,ThomasM(2004).“AlfredMarshallandthequantitythe-
oryofmoney”.In:
Jackson, Jerry (2010). “Improving energy efficiency and smart grid
programanalysiswithagent-basedend-useforecastingmodels”.
In:EnergyPolicy38.7,pp.3771–3780.
Jensen, Henrik Jeldtoft (1998). Self-organized criticality: emergent com-
plex behavior in physical and biological systems. Vol. 10. Cambridge
universitypress.
Jiang, XF, TT Chen, and B Zheng (2014). “Structure of local interac-
tionsincomplexfinancialdynamics”.In:Scientificreports4.
Jorion, Philippe (1996). “Risk2: Measuring the risk in value at risk”.
In:FinancialAnalystsJournal52.6,pp.47–56.
Joskow,PaulLandRichardSchmalensee(1983).“Marketsforpower:
ananalysisofelectricutilityderegulation”.In:
Kaplan, Stan (1997). “The words of risk analysis”. In: Risk analysis
17.4,pp.407–417.
King, Jack Leon (2001). Operational risk: measurement and modelling.
Wiley.
Koller, Tim, Marc Goedhart, David Wessels, et al. (2010). Valuation:
measuringandmanagingthevalueofcompanies.Vol.499.johnWiley
andsons.
Kraus, Alan and Robert H Litzenberger (1973). “A state-preference
modelofoptimalfinancialleverage”.In:Thejournaloffinance28.4,
pp.911–922.
Krause,HandDayanandArora(2010).KeyPerformanceIndicators.
Krause,Thiloetal.(2006).“AcomparisonofNashequilibriaanalysis
and agent-based modelling for power markets”. In: International
JournalofElectricalPower&EnergySystems28.9,pp.599–607.BIBLIOGRAPHY 143
Krawczyk, Jacek B and Stanislav Uryasev (2000). “Relaxation algo-
rithms to find Nash equilibria with economic applications”. In:
EnvironmentalModeling&Assessment5.1,pp.63–73.
Kuznetsova,Elizaveta(2014).“Microgridagent-basedmodellingand
optimization under uncertainty”. PhD thesis. Université de Ver-
saillesSaint-Quentin-en-Yvelines.
Kwapien´,JarosławandStanisławDroz˙dz˙ (2012).“Physicalapproach
tocomplexsystems”.In:PhysicsReports515.3,pp.115–226.
Lam,Jamesetal. (2006).“Emergingbestpracticesindevelopingkey
risk indicators and ERM reporting”. In: Japan: James Lam and As-
sociates.
LeBaron, B (2005). “Agent-based computational finance. Handbook
of Computational Economics, Volume 2: agent-based computa-
tionaleconomics”.In:Elsevier,AmsterdamLuxT,MarchesiM(2000)
Volatility clustering in financial markets: A micro-simulation of inter-
actingagents.IntJTheorApplFinance3,675702Nagakura.
Leitch,Matthew(2010).“ISO31000:2009-Thenewinternationalstan-
dardonriskmanagement”.In:RiskAnalysis30.6,pp.887–892.
Levy, David (1994). “Chaos theory and strategy: Theory, application
andmanagerialimplications”.In:Strategicmanagementjournal15,
pp.167–167.
Li, Ningzhong (2015). “Performance measures in earnings-based fi-
nancialcovenantsindebtcontracts”.In:AvailableatSSRN1966112.
LI, Peiyu and Guihua LIN (2013). “Solving a Class of Generalized
Nash Equilibrium Problems”. In: Journal of Mathematical Research
withApplications33.3,pp.372–378.
Liu,MinandFelixFWu(2007a).“Portfoliooptimizationinelectricity
markets”.In:ElectricPowerSystemsResearch77.8,pp.1000–1009.
— (2007b). “Risk management in a competitive electricity market”.
In: International Journal of Electrical Power & Energy Systems 29.9,
pp.690–697.
Liu, Min, Felix F Wu, and Yixin Ni (2006). “A survey on risk man-
agement in electricity markets”. In: 2006 IEEE Power Engineering
SocietyGeneralMeeting.IEEE,6–pp.
Malandrino,Francescoetal.(2015).“Agame-theoryanalysisofcharg-
ing stations selection by EV drivers”. In: Performance Evaluation
83,pp.16–31.
Malkiel, Burton G and Eugene F Fama (1970). “Efficient capital mar-
kets: A review of theory and empirical work”. In: The journal of
Finance25.2,pp.383–417.
Manco, Oscar, Oscar Botero, and Santiago Medina (2016). “Risker:
Platform Implementation of Complex System Model for Finan-
cial Risk Management in Energy Markets”. In: Procedia Computer
Science83,pp.1078–1083.
Medina, Santiago (2006). “Estado de la cuestión acerca del uso de la
lógica difusa en problemas financieros”. In: Cuadernos de adminis-
tración19.32,pp.195–223.144 BIBLIOGRAPHY
Medina, Santiago and Oscar Manco (2007). “Diseño de un sistema
experto difuso: evaluación de riesgo crediticio en firmas comi-
sionistas de bolsa para el otorgamiento de recursos financieros”.
In:EstudiosGerenciales23.104,pp.101–129.
Medina,SantiagoandJulianMoreno(2007).“RiskevaluationinColom-
bian electricity market using fuzzy logic”. In: Energy Economics
29.5,pp.999–1009.
Minas, Ministerio de (2013). Energía Eléctrica - Memorias del congreso
delarepública.RepúblicadeColombia.
Nanduri, Vishnu and Tapas K Das (2009). “A survey of critical re-
searchareasintheenergysegmentofrestructuredelectricpower
markets”.In: InternationalJournal of Electrical Power &Energy Sys-
tems31.5,pp.181–191.
Neuhoff, Karsten et al. (2005). “Network-constrained Cournot mod-
elsofliberalizedelectricitymarkets:thedevilisinthedetails”.In:
EnergyEconomics27.3,pp.495–525.
Neumann, Ludwig Johann and Oskar Morgenstern (1947). Theory of
games and economic behavior. Vol. 60. Princeton university press
Princeton.
Newman, David E et al. (2011). “Exploring complex systems aspects
of blackout risk and mitigation”. In: Reliability, IEEE Transactions
on60.1,pp.134–143.
Newman, Mark EJ (2003). “The structure and function of complex
networks”.In:SIAMreview45.2,pp.167–256.
NlKAIDO, Hν¨KUKANE and Kazuo Isoda (1955). “Note on nonco-
operative convex games”. In: Henry A. Antosiewicz, A theorem on
alternativesforpairsofmatrice641FVAtkinson,Onsecond-ordernon-
linearoscillation643FrankHerbertBrownell,III,Fourieranalysisand
differentiationoverreal,p.807.
Overbye,ThomasJandDouglasAWiegmann(2005).“Reducingthe
risk of major blackouts through improved power system visual-
ization”. In: presentation at 15th Power System Computation Confer-
ence(PSCC),LiegeBelgium.
Pakes,Ariel(2015).“MethodologicalIssuesinAnalyzingMarketDy-
namics”.In:
Parmenter,David(2015).Keyperformanceindicators:developing,imple-
menting,andusingwinningKPIs.JohnWiley&Sons.
Power, Michael et al. (2009). “Reputational risk as a logic of organiz-
inginlatemodernity”.In:Organizationstudies30.2-3,pp.301–324.
Purdy,Grant(2010).“ISO31000:2009-settinganewstandardforrisk
management”.In:Riskanalysis30.6,pp.881–886.
Renn, Ortwin and Andreas Klinke (2004). “Systemic risks: a new
challengeforriskmanagement”.In:EMBOreports5.1S,S41–S46.
Repullo, Rafael and Jesus Saurina Salas (2011). “The countercyclical
capitalbufferofBaselIII:Acriticalassessment”.In:
Rivier, Michel et al. (2000). “Estudio cargo por capacidad en Colom-
bia”.In:UniversidadPontificiaComillas,Madrid,España.BIBLIOGRAPHY 145
Sandoval, Ana María et al. (2004). Monografía del sector de electricidad
ygascolombiano:condicionesactualesyretosfuturos.DNP.
Saunders, Anthony, Marcia Millon Cornett, and Patricia Anne Mc-
Graw (2006). Financial institutions management: A risk management
approach.Vol.8.McGraw-Hill/Irwin.
Scandizzo, Sergio (2005). “Risk mapping and key risk indicators in
operational risk management”. In: Economic Notes 34.2, pp. 231–
256.
Schiffer,Hans-Wilhelm(2008).“WECenergypolicyscenariosto2050”.
In:EnergyPolicy36.7,pp.2464–2470.
Sioshansi, Fereidoon P (2002). “The emergence of trading and risk
management in liberalized electricity markets”. In: Energy Policy
30.6,pp.449–459.
Solé,RicardoVicenteandSusannaCManrubia(2009).Ordenycaosen
sistemascomplejos:aplicaciones.Vol.2.Univ.Politèc.deCatalunya.
Sornette,AandDSornette(1989).“Self-organizedcriticalityandearth-
quakes”.In:EPL(EurophysicsLetters)9.3,p.197.
Stavridou,HeleniandChristinaSolomonidou(1989).“Physicalphenomena–
chemical phenomena: do pupils make the distinction?” In: Inter-
nationalJournalofScienceEducation11.1,pp.83–92.
Stoft, Steven (2002). “Power system economics”. In: Journal of Energy
Literature8,pp.94–99.
Sweeting, Andrew (2007). “Market power in the England and Wales
wholesaleelectricitymarket1995–2000*”.In:TheEconomicJournal
117.520,pp.654–685.
Tappeiner,FlorianTetal.(2010).Structureanddeterminantsoffinancial
covenantsinleveragedbuyouts.München.
Tesfatsion,Leigh(2003).“Agent-basedcomputationaleconomics:mod-
eling economies as complex adaptive systems”. In: Information
Sciences149.4,pp.262–268.
Tirole,Jean(2010).Thetheoryofcorporatefinance.PrincetonUniversity
Press.
Toro,JMRevellóde(2004).Lavaloracióndelosnegocios.
Tremblay,CarolHortonandVictorJTremblay(2011).“TheCournot–
Bertrand model and the degree of product differentiation”. In:
EconomicsLetters111.3,pp.233–235.
Tumminello,Micheleetal.(2005).“Atoolforfilteringinformationin
complex systems”. In: Proceedings of the National Academy of Sci-
encesoftheUnitedStatesofAmerica102.30,pp.10421–10426.
Tushar,Wayesetal.(2013).“Prioritizingconsumersinsmartgrid:En-
ergymanagementusinggametheory”.In:Communications(ICC),
2013IEEEInternationalConferenceon.IEEE,pp.4239–4243.
Valencia, Beatriz López, Diego Arboleda Jaramillo, and Interconex-
ión Eléctrica SAESP (2010). “Integraciyn del manejo de riesgo e
incertidumbre en la planeaciyn financiera de empresas de trans-
misiyndeenergta”.In:RevistaCIERN 54,p.4.
Vanderbei,RobertJ(2014).Linearprogramming.Springer.146 BIBLIOGRAPHY
Wang,Chengwei,CelsoGrebogi,andMuriloSBaptista(2016).“Mod-
elling,controlling,predictingblackouts”.In:arXivpreprintarXiv:1603.01509.
Weidlich, Anke and Daniel Veit (2008). “A critical survey of agent-
based wholesale electricity market models”. In: Energy Economics
30.4,pp.1728–1759.
Whited, Toni M and Guojun Wu (2006). “Financial constraints risk”.
In:ReviewofFinancialStudies19.2,pp.531–559.
Wiszniewska-Matyszkiel,Agnieszkaetal.(2008).“Stockmarketasa
dynamicgamewithcontinuumofplayers”.In:ControlandCyber-
netics37.3,pp.617–647.
Wolfram,CatherineD(1999).“MeasuringduopolypowerintheBritish
electricity spot market”. In: American Economic Review, pp. 805–
826.
Wyman,O(2011).DinamicFinancial-planningGlobalRiskandTrading.
MarshandMcLennanCompany.
Xiao, Mi et al. (2015). “A new methodology for multi-objective mul-
tidisciplinary design optimization problems based on game the-
ory”.In:ExpertSystemswithApplications42.3,pp.1602–1612.
Yang,Yang,JingGu,andZongfangZhou(2015).“ComplexityStudy
of the Credit Risk of a Business Group”. In: Discrete Dynamics in
NatureandSociety2015.
Yao,Jian,IlanAdler,andShmuelSOren(2008).“Modelingandcom-
puting two-settlement oligopolistic equilibrium in a congested
electricitynetwork”.In:OperationsResearch56.1,pp.34–47.
Young,David,StephenPoletti,andOliverBrowne(2014).“Canagent-
basedmodelsforecastspotpricesinelectricitymarkets?Evidence
from the New Zealand electricity market”. In: Energy Economics
45,pp.419–434.
Yousefi, Shaghayegh, Mohsen Parsa Moghaddam, and Vahid Johari
Majd (2011). “Optimal real time pricing in an agent-based retail
market using a comprehensive demand response model”. In: En-
ergy36.9,pp.5716–5727.
Yu,Nanpeng,AbhishekSomani,andLeighTesfatsion(2010).“Finan-
cial risk management in restructured wholesale power markets:
Conceptsandtools”.In:PowerandEnergySocietyGeneralMeeting,
2010IEEE.IEEE,pp.1–8.
Zhao,JialinandSangBaumKang(2015).“Co-SimulationofRiskFac-
torsinPowerMarkets”.In:AvailableatSSRN2614664.
Zhou, Zhi, Wai Kin Victor Chan, and Joe H Chow (2007). “Agent-
basedsimulationofelectricitymarkets:asurveyoftools”.In:Ar-
tificialIntelligenceReview28.4,pp.305–342.