2020 IEEE Symposium Series on Computational Intelligence (SSCI)
on Computational Intelligence for Financial Engineeringand Economics (CIFEr) http://www.ieeessci2020.org/

Paper ID: #30

An agent-based model for
designing a financial market that works well
Takanobu Mizuta

SPARX Asset Management Co., Ltd.
Mail: mizutata[at]gmail.com
HP: https://mizutatakanobu.com

Note that the opinions contained herein are solely those of the authors and do notnecessarily reflect those of SPARX Asset Management Co., Ltd.

You can download this presentation material fromhttps://mizutatakanobu.com/2020CIFErb.pdf

1This presentation showed a philosophy of an agent-based artificial market model.
Why models are needed? How models should be? In the first place, what is a model?
We should understand what is a model deeper for healthy discussion using a model.
I will try to clear up a common misunderstanding for a model.
After the discussion, I will review the case, investigating tick size reduction using a model.

2(1) An artificial market model = an agent-based model for a financial market(2) Suitable complexity, advantages and disadvantages(3) Case study: tick size reduction(4) Conclusion3

(1) An artificial market model = an agent-based model for a financial market(2) Suitable complexity, advantages and disadvantages(3) Case study: tick size reduction(4) Conclusion

4

Importance and difficulty of market design

Peoplehave been able to develop advanced economies
by cooperating to exchange goods for money

Creation of any industry requires “investment” to first purchase or build tools to make goods
enables smooth investment

FinancialMarketCreates Better Goods Better Service

Two Extreme Opinions

No regulation is Best?

Destroy a Society?

Both is Wrong“A market works well only if it is well designed”
Proper rules and regulations are required(By the economist John McMillan, who used game theory to investigate many markets)
5John McMillan, 2002
https://wwnorton.com/books/Reinventing-the-Bazaar/“A market works well only if it is well designed”
Market design determines whether
a market works well or badly
Very important forDeveloping economy

A market is a highly complex system.
It is at least as complex as the systems
studied by physicists and biologists
Very difficult and complex system“Economies are complex systems in which the simple, microscopic
components consist of people buying and selling goods, and thecollective behavior is the complex, hard-to-predict behavior ofmarkets as a whole, such as fluctuations in stock prices”
Changing detailed rules, even ones that seem trivial, sometimes causes
unexpected large impacts and side effects.

both God and the devil are in the details
Designing a market well is very important for developing an
advanced economy, but not easy.

6

Melanie Mitchell, 2009https://global.oup.com/academic/product/complexity-9780195124415

Agent-Based Model succeeded to explain Social Complex Systems other than Financial Market

For examples,• Making Evacuation Route of new building for Fire and/or Terror• Investigating for effects of building new roadway to traffic jam• Discussing how spread COVID-19
and so on
There are many many studies succeeded explain thephenomena of social complex systems

7

An artificial market model = an agent-based model for a financial market

Virtual and Artificial financial Market built on Computers
ModelsIncludeAgents (Artificial Investors)＋
Price Mechanism (Artificial Exchange)
Order

Price
Mechanism(Exchange)

Agent(Investor)

Each Agent determines anorder by some rules,
Price Mechanism gather
agents orders anddetermines Market Price

Determination market priceComplete Computer Simulation needing NO Empirical Data
✓ can discuss on the mechanism between the micro-macro feedback✓ can be conducted to investigate situations that have neveroccurred in actual financial markets✓ can be conducted to isolate the direct effect of changing rules
8

NATURE/SCIENCE articles argued Importance of Simulations⚫ Farmer and Foley (2009) NATURE, Vol. 460, No. 7256, pp. 685-686.
https://www.nature.com/articles/460685a

In today’s high-tech age, one naturally assumes that US President Barack Obama’s economic teamand its international counterparts are using sophisticated quantitative computer models to guide us
out of the current economic crisis. They are not. There is a better way: agent-based models.
⚫ Battiston et al. (2016) SCIENCE, Vol. 351, Issue 6275, pp. 818-819.
http://science.sciencemag.org/content/351/6275/818

Traditional economic theory could not explain, much less predict, the near collapse of the financial
system and its long-lasting effects on the global economy. Since the 2008 crisis, there has been
increasing interest in using ideas from complexity theory to make sense of economic and financial
markets.
These articles argued that

Traditional economic theory could not explain, muchless predict, the near collapse of the financial system

Agent-Based Model is needed

9Criticism to Standard Economic Model and arguing needs of Agent-Based Model

Richard Bookstaber
Expert of risk management at Investment Banks and Hedge Funds
Famous for The author of “A Demon of Our Own Design” isnoted for its forecasting of the financial crisis of 2008

Standard Economic Model did not prevent Financial
Crises of 2008. An Agent-Based Model will prevent
the Crises.
Arguing importance of using Agent-Based Model
when we discuss how prevent the Financial Crises
Richard Bookstaber, 2017https://press.princeton.edu/books/hardcover/9780691169019/the-end-of-theory10

Practical Persons have began to use Agent-Based Model to solve Urgent Real Problem
Regulators, Central Bankers, Stock Exchanges
JPX Working Papers Series
JPX(parent com of Tokyo Stock Exchange) shows Working Papers,
10 papers of all 34 are Agent-Based Studies
Reduction of Tick Size, Frequently Batch Auction,
Suitable Latency of Exchange System, and so on
https://www.jpx.co.jp/english/corporate/research-study/working-paper/index.html

So many other Examples,Working Paper by Bank of Japan
Toshiyuki Sakiyama and Tetsuya Yamada, Market Liquidity and Systemic Risk in Government Bond
Markets: A Network Analysis and Agent-Based Model Approachhttps://www.imes.boj.or.jp/research/abstracts/english/16-E-13.html
Project by EU
Integrated Macro-Financial Modelling for Robust Policy Design Work Package 7: Bridging agent-based
and dynamic-stochastic-general-equilibrium modelling approaches for building policy-focused macrofinancial models https://cordis.europa.eu/project/id/612796/reporting
My review
Takanobu Mizuta, A Brief Review of Recent Artificial Market Simulation Studies for Financial Market
Regulations And/Or Rules, SSRN Working Paper Series https://ssrn.com/abstract=2710495

11

(1) An artificial market model = an agent-based model for a financial market(2) Suitable complexity, advantages and disadvantages(3) Case study: tick size reduction(4) Conclusion

12

An agent-based model explaining a complex system

A financial market is highly complex system where a simple summation of microprocesses (trader behaviors) never explains macro phenomena (price formation).

Separately investigating macro phenomena and micro processes
unclearly explains complex systems where macro phenomena andmicro processes interact.
A mathematical model
An empirical study

cannot directly treat nor clearly explain the interactions

An Agent-Based Modelcan directly treat and clearly explain the interactions
Because…

13

A mathematical model
An empirical study

An Agent-Based Model

Macro Phenomena

Macro Phenomena
Price Formation
Simulation Feedback

As a result

Treat
Directly &Interactively

Micro Process
Agents Behavior

Simple Modelling

can directly treat andclearly explain the interactions

Price Formation
NO simple summation
No explains

Precious
Modelling

Treat
Separately

Micro Process
Traders Behavior

Precious
Modellingcannot directly treat nor
clearly explain the interactions

14

Advantages and Disadvantages of Agent-Based Model

Happened

Will happen

Empirical
Study

Agent-Based
Model

Outputs of an empirical study are includedin the area that has happened in a real
financial market. The advantage of anempirical study is outputs exclude the allarea not happening in the past or future.
The disadvantage, however, is outputs
exclude any area happening in the future.

The advantage of an agent-basedmodel is outputs include the part of
the area happening in the future.
The disadvantage, however, is
outputs include the part of area nothappening in the past or future.

An agent-based model just outputs “possible” results to understand themechanism of a market. Discussing whether the results will occur or not needs
other methods, e.g., an empirical study and a mathematical model.
15

Advantage: directly treat Positive Feedback (Self-Fulfilling Prophecy)

ExpectingSomeone buy
Higher Price

It convincesme

Positive Feedback
Self-Fulfilling Prophecy
Self-Reinforcing Process

Meet myExpectation

I Buy

Price raises
16Collaborate to mutually compensate for their disadvantages

Environment happening in the future

Macro
Phenomena

Empirical Study
Financial Engineering
Macro Modeland so on

Understanding
Interaction
Mechanism

Agent-Based
Model
Verified & Validated
by other methods
VerifyValidate
Simulation Agent-Model
result

Micro
Process

Behavioral Economics
Experimental Economics
Neuroeconomics
and so on

Discussing the outputs of an agent-based model always needs knowledge
given by empirical studies and mathematical models. A market that works wellshould be designed by not one but several methods, and the methods shouldcollaborate to mutually compensate for their disadvantages.
17What is a role of Simulation Models? Suitable complexity?

Discussing the philosophy of models andsimulations.
“What is a role of Simulation Models? ”“What is a model?”,“How complexity is suitable for the model?”Very very good book.
I think all researcher who use some model should read this bookfor healthy discussion using models.
(Following some slides, I will introduce the discussion of the book)

Simulation and Similarity Using Models to Understand the World, 2012https://global.oup.com/academic /product/9780199933662

18

Which ‘’map’’ explains the access better?
Some of maps are “models” of the real geography for understanding an access.

Very different from the real, however,very good explaining the access.

Very similar to the real, however,very bad explaining the access.

must shave non-investigating features from the model
Different investigations, different shaving parts.

19

Role of Model (in the case of Agent-Based Artificial Market Model)

InvestorA

Investor
B

Investor
C

Inherit Only Important Properties(Behaviors, Algorithms) for Investigating Phenomena

Other Investigating
Phenomena,
Other Important Properties,
Other Good Models

Never Real-Existing Investor
For Understanding Properties
of Real-Existing Investors

Model ofInvestors e.g.: Fashion Model: Understanding Closes
Model Home: Understanding Home

An Aim is to understand how Important Properties (Behaviors, Algorithms)
affect Investigating Macro Phenomena and play Roles in System.

It is NOT aim Replicating real-existing Investors A, B and C.
It is aim Understanding real-existing Investors.
The simplicity of the model is very important because unnecessary replication of macro phenomena
leads to models that are overfitted and too complex. Such models prevent understanding anddiscovery of mechanisms affecting price formation because of the increase in related factors.

Other Focusing Phenomena, Other Good Models; no model good for anything exist

20

Example of equation model cannot but simulation model can (Schelling Model)
Party with Students(#) and Professors(@)
#
# #
#
@
@ @
#
#
@

# @ #
# @
@
@
#
# @ # @
@ # @ @# # #@ # @ #@

Rules:* around me (8pixs)
with more 1/3 myequals -> not move
* No -> move
After many steps,,,

@
# @
@ #
# @
@
@
@
#

Mod. rules:＃:need one more equal@:need one less equal# # # #
# # # #
# # # #@ # @@ @ @ #
#
@ #
@
@

@
@ @

@
@
@

@
@
#
#
#

The space of #is smaller

@
@
@ @
@
# @
# #

Micromotives and Macrobehavior, 2006
http://books.wwnorton.com/books/978-0-393-32946-9/

#
#
#
@

#
#
#
@
@
@

@ @

#
# @
@ @
@
@ #
# #
# #

@ # #
@ @ #
@
@ @
@ @ @
# @ @
# #
#

#
#
@
@

# and @ have been separated
The segregation occurs even if we want not to be heavily
minority. We do NOT hate other kinds.

The purpose of simulation is understanding the reasons andmechanism, not forecasting the final distribution.
Where are tables? How much they eat? Where are assistant professors?
Is the party place square? Are behaviors of people too simple?
---- Silly questions for the purpose of simulation.
prevent our understanding the mechanism.

Simplifying depends on that we want to understandSchelling recommended you simulate this manually using coins to understand what is simulation model.

21

We want know a relationship between
Micro Process:
Deciding Orders, Rules of Exchange& Macro Phenomena: Price Formation

Mathematical Model
Macro Model

Stock
MarketCountry Ａ
Bond
MarketCountry A
Stock
MarketCountry B

Replicate Only
Important Properties

can treat only this region

Price
Formation(Simulation
Result)Model ofInvestors

Deciding
OrdersInherit Only
Important Properties

Role of Model (cont.)

InvestorA
Investor
B

InvestorModel of (Algorithms)
C
Exchange
ChangeRules
Matching
OrdersWe want know
(Aggregation of
Algorithms)

a relationshipbetween them22

(1) An artificial market model = an agent-based model for a financial market(2) Suitable complexity, advantages and disadvantages(3) Case study: tick size reduction(4) Conclusion

23

Here, I very briefly introduce Mizuta et. al. 2013 as a typical study investigating the designof a financial market using an artificial market model.
Mizuta et. al. 2013, “Investigation of Relationship between Tick Size and Trading Volume of Markets using
Artificial Market Simulations”, JPX working Paper Vol. 2
https://www.jpx.co.jp/english/corporate/research-study/working-paper/index.html

24What is Tick Size?
95.0

Market Price

94.0
93.0
92.0
91.0
Minimum Increment: \1 ⇒ Tick Size: 1%

90.0

Minimum Increment: \0.1 ⇒ Tick Size: 0.1%

15:00

14:00

13:00

11:00

10:00

09:00

89.0

time (hh:mm)

Difference of 1% Return is Serious Problem for some Investors⇒ They prefer Stock Market has Smaller Tick Size
25

Normal Agent(NA)The model of Mizuta (2013) is based on Chiarella (2002).
The model is satisfied with stylized facts (statistical characteristics
observed in actual financial markets).

Expected Return of each NA

Technical

Pf
1 
t
t 
 w1, j log t + w2, j rh, j + w3, j j r =P
i wi, j 

t
e, j

Fundamental

noise

All NAs use this same equation to obtain an expected return,however, because w is different each agents, expected returns aredifferent each agents. This leads heterogeneous (many order prices
are diversified) although the model is simple.

The simplicity of the model is very important.
Models include too many related factors prevent
understanding and discovery of mechanisms affecting
price formation.

26

Market Selection Model
Initial Trading
Volume Share: 90%
Tick Size: Large
Maket A

Initial Trading
Volume Share: 10%
Tick Size: Small
Market B
Market Order： Choose themarket list best priceAgentsLimit Order： Allocate on basisof Historical Trading Volume
Share of each market

Market Order： buy or sell at the best available price, immediately
Limit Order： buy or sell at a specific price or better,
waiting opposite Market Orders
27

Tick Size of Market B is 0.01%, Tick Size is not small

Tick Size of Market A is large,
Market A is taken trading volume share28

Tick Size of Market B is 0.0001%, Tick Size is enough smallMarket B can hardly take the share in spite that Tick Size of Market A
is very larger than that of Market B

29

Tick Size Condition Not to Move Share
Market share of
Tick sizes of market B
market A at 500
0.001% 0.002% 0.005% 0.01% 0.02% 0.05% 0.1%
0.001%
90%
92%
94%
97%
99% 100% 100%
0.002%
89%
91%
93%
97%
99% 100% 100%
84%
87%
92%
96%
99% 100% 100%Tick sizes 0.005%
of market
0.01%
77%
78%
83%
92%
98% 100% 100%
A
0.02%
54%
54%
59%
70%
93% 100% 100%
0.05%
5%
5%
5%
6%
23%
93% 100%
0.1%
0%
0%
0%
0%
0%
0% 94%

Condition Not toMove Share⊿PB>⊿PA

Condition to
Rapidly Move Share t < ⊿PAor

1/10  t > ⊿PA t = 0.05%30

 t < ΔPA
Impossible
to trade atmarket A

Marketprice

Tick size ofmarket A
time

Market A never represents⇒ Orders move to market B
movement of market prices.

 t > ΔPA

Marketprice

Enoughresolution
at market A
Market A represents them.

Tick size ofmarket A
time⇒ not need market B

An Aim is to understand how Important Properties (Tick-Size) affectInvestigating Macro Phenomena (Market Share) and play Roles in System.

It is NOT aim Replicating real-existing Investors and Market Prices,
but understanding mechanism of the system.

(1) An artificial market model = an agent-based model for a financial market(2) Suitable complexity, advantages and disadvantages(3) Case study: tick size reduction(4) Conclusion

32

This study showed a philosophy of an agent-based artificial market model.
Why models are needed? How models should be? In the first place, what is a model?
We should understand what is a model deeper to discus healthy using a model.
I will try to clear up a common misunderstanding for a model.
Someone may think tick size reduction is a trivial matter for a financial market. This is,however, important and should not be underestimated. Changing detailed rules sometimes
causes unexpected large impacts and side effects. John McMillan illustrated this nature as“both God and the devil are in the details''. Detailed design can determine whether afinancial market develops or destroys an advanced economy. Designing a market well isvery important for developing and maintaining an advanced economy, but not easy.

I hope that more agent-based artificial market models will contribute todesigning a financial market that works well to further develop and maintainadvanced economies.

33

An agent-based model for designing a financial market that works well
Takanobu Mizuta
Paper ID: #30✓ Designing a financial market that works well is very important for developing and maintaining an
advanced economy, but is not easy because changing detailed rules, even ones that seem trivial,
sometimes causes unexpected large impacts and side effects.
✓ A computer simulation using an agent-based model can directly treat and clearly explain such complex
systems where micro processes and macro phenomena interact. Recently, an artificial market model,
which is an agent-based model for a financial market, has started to contribute to discussions on rules
and regulations of actual financial markets.
✓ We should understand what is a model deeper for healthy discussion using a model. I tried to clear up acommon misunderstanding for a model. Why models are needed? How models should be? In the firstplace, what is a model?
✓ The purpose of simulation is understanding the reasons and mechanism, not exactly forecasting thereal world. The simplicity of the model is very important because unnecessary replication of macro
phenomena leads to models that are overfitted and too complex. Such models prevent understanding
and discovery of mechanisms affecting price formation because of the increase in related factors. We
must shave non-investigating features from the model. Different investigations, different shaving parts.
✓ I briefly introduced an artificial market model to design financial markets that work well and describe aprevious study investigating tick size reduction. I hope that more artificial market models will contributeto designing financial markets that work well to further develop and maintain advanced economies.

Appendix

35

Verification: Stylized Facts
The purpose of simulation is understanding the reasons and mechanism,
not replicating ALL Stylized Facts
The simplicity of the model is very important because unnecessary replication of macro phenomena
leads to models that are overfitted and too complex. Such models prevent understanding anddiscovery of mechanisms affecting price formation because of the increase in related factors.
Many empirical studies, e.g., Sewell 2006 have shown that both stylized facts (fat-tail and volatilityclustering) exist statistically in almost all financial markets.
Conversely, they also have shown that only the fat-tail and volatility-clustering are stable for any asset
and in any period because financial markets are generally unstable.

Fat-tail

1 to 100

kurtosis of price returns is positive

Volatility-clustering

0 to 0.2

square returns have a positive auto-correlation

The magnitudes ofthese values are
unstable and vary
greatly depending on
the asset and/or
period.

For the above reasons, an artificial market model should replicate these values as significantly positive
and within a reasonable range as I mentioned. It is not essential for the model to replicate specificvalues of stylized facts because the values of these facts are unstable in actual financial markets.
36

Stylized Facts

The model of Chiarella (2002) is very simple but replicates long-term statistical characteristics observed in actual
financial markets: a fat tail and volatility clustering.
In contrast, Mizuta (2013) replicates high-frequency micro structures, such as execution rates, cancel rates, andone-tick volatility, that cannot be replicated with the model of Chiarella (2002).
The simplicity of the model is very important for this study, because unnecessary replication of macro phenomena
leads to models that are overfitted and too complex. Such models prevent understanding and discovery ofmechanisms affecting price formation because of the increase in related factors.

37

Detail of Expected Return
j: agent number (1,000 agents)
ordering in number ordert: tick time

Expected Return of each NA

Historical Returnt − jr = log(P / P
t
h, j

t

)

Technical

Pf
1 
t
t 
 w1, j log t + w2, j rh, j + w3, j j r =P
i wi, j 

t
e, j

wi , j and  j

PfFundamental Price

Random ofUniform Distribution

Pt

Market Price at t

wi , jji=1,3: 0～1
i=2: 0～10
0～10000

noise

Fundamental

Parameters for agents

10000 = constantExpected Price of each NA tj

Random ofNormalDistribution
Average=0
σ=3%Pet, j = Pt exp(ret, j )38

Fundamental and Technical Strategies
Fundamental Strategy
Fundamental Price ＞ Market Price -> Expect + return
Fundamental Price < Market Price -> Expect - return
Technical Strategy
Historical Return ＞ 0 -> Expect + return
Historical Return < 0 -> Expect - return
Technical
Strategy

Fundamental
Price
MarketPrice

Fundamental
Strategy39Order Price and Buy or Sell
Price

Order Price of each NA
t
o, j

P

Sell(one unit)
Random(GaussDistribution)

Expected Price of each NA
t
t
t
e, j
e, j

P

= P exp(r)

Buy(one unit)

To replicate many waiting limit orders,
order price is scattered around expected price
NA places one buy order when order price > expected price
NA places one sell order when order price < expected price40