Euro area banks’ sensitivity to changes in carbon price.
Date: 2022-05-02
Institutions: European Central Bank
Subjects: banking, climate change policy, economic transition, euro area, financial risk, price of energy, reduction of gas emissions, type of business

Marco Belloni, Friderike Kuik, Luca Mingarelli 

Working Paper Series 

Euro Area banks’ sensitivity 
to changes in carbon price 

No 2654 / March 2022 

Disclaimer: This paper should not be reported as representing the views of the European Central Bank 
(ECB). The views expressed are those of the authors and do not necessarily reflect those of the ECB. 

 
 
Abstract

In recent years there has been growing attention on the risks posed by climate change.

One relevant question for ﬁnancial stability is to which extent the materialisation of transition

risks emerging from the sudden implementation of climate change mitigation policies would

impact the ﬁnancial system. In this paper we analyze the eﬀects of changes in carbon price

on the European banking system. We assess this climate change transition risk through a

banking sector contagion model where ﬁrms are negatively impacted by an increase in carbon

prices. Using a unique granular dataset we evaluate the consequences of a combination of

diﬀerent increases in carbon prices and ﬁrm emission reduction strategies. We ﬁnd that

taking early policy action, implying more gradual changes in carbon prices, is not expected

to lead to adverse impacts on the banking system, especially if ﬁrms reduce their emissions

eﬃciently. Conversely, a disorderly, abrupt transition to a low carbon economy requiring

very high sudden changes in carbon prices might have disruptive eﬀects on the ﬁnancial

system, especially if ﬁrms fail to reduce their emissions.

Keywords:  Empirical  Banking,  Financial  Networks,  Climate  Change,  Transition  Risk.

JEL  Codes:  Q48,  Q54,  Q58.

ECB Working Paper Series No 2654 / March 20221Non-technical summary

To meet the goals of the Paris Agreement, policymakers are currently adopting measures to

mitigate climate change, aiming to transition to low carbon economies. Also central banks and

ﬁnancial institutions have entered the debate, discussing the eﬀects of climate change, and the

eﬀects of climate change mitigation strategies, onto the ﬁnancial system. In particular, if not

well addressed and measured, an abrupt and disorderly transition can have repercussions on

the ﬁnancial system. Some ﬁrms might suﬀer losses due to e.g.

increases in energy prices,

implementation of carbon taxes or shifts in consumer preferences to less polluting options.

Therefore, the transition to a greener economy might put some ﬁrms out of business and lead

others to the brink of bankruptcy. Banks, as a consequence, can face losses through their

exposures to these ﬁrms, which can weaken the stability of the ﬁnancial system.

This paper analyses the risks posed to the ﬁnancial system stemming from a transition to

a low carbon economy, focusing on the impact of changes in carbon prices. We do so in a

forward-looking manner, using a banking system contagion model, where banks are connected

through loans and securities exposures, and where ﬁrms suﬀer from rises in carbon prices that

are absorbed on their balance sheets and therefore may aﬀect their likelihood to default. The

impact of the carbon price increase on ﬁrms likelihood to default depends on the level of carbon

emissions produced by each ﬁrm, on their leverage ratio, and on their ability to pass carbon

prices onto their customers. We run simulations for diﬀerent scenarios of carbon price increases

and diﬀerent assumptions on ﬁrm emission reductions.

Our results suggest that under more ambitious ﬁrm emissions reduction strategies, the losses

borne by the ﬁnancial system would be contained also for large increases in carbon prices. At

the same time, our results also suggest that if no action is taken, and ﬁrms keep their emissions

constant, abrupt and large increases in carbon prices may lead to severe banking system losses

which could reach up to 40% more compared to a baseline situation where no policy action is

taken.

Therefore, the analysis suggests that in order to hedge themselves from transition risks,

banks might have to restrict their lending to less polluting ﬁrms, lend to ﬁrms with ambitious

emissions reduction targets or help ﬁrms in transitioning to low carbon business models. In this

context, policy measures are pivotal to require ﬁrms to disclose the direct and indirect emissions

produced, as well as veriﬁable strategies to reduce them. Policy measures should target banks

ECB Working Paper Series No 2654 / March 20222too, which should disclose not only their carbon footprint, but especially the climate risks

connected to their exposures. Finally, regulators may need to implement further prudential

measures to prevent the built-up of banking system losses or pockets of risks through bank

exposures to ﬁrms not adapting to a greener economy.

ECB Working Paper Series No 2654 / March 202231 Introduction

Current global warming has exceeded 1◦C above pre-industrial levels, and impacts of human-

made climate change have already materialized (IPCC, 2021). The period 2015-2019 has been

the warmest ﬁve-year-period on record globally (WMO, 2019; ECMWF, 2020), and a number

of recent extreme events have been ampliﬁed by climate change (see, e.g. Otto et al., 2020). To

mitigate the eﬀects of climate change, the Paris Agreement aims at limiting the increase in global

temperature in 2100 to well below 2◦C above pre-industrial levels, pursuing eﬀorts to limiting it

to 1.5◦C. The Paris Agreement also promotes low carbon, climate resilient growth and making

ﬁnance ﬂows consistent with this pathway (UNFCC, 2015; NGFS, 2019). Several countries and

regions have committed to reach carbon neutrality or signiﬁcant emission reductions within the

next 30 years1.

Climate policies are therefore being designed, aimed at limiting emissions through, for exam-

ple, increasing the price of carbon (e.g. carbon tax, cap and trade schemes for emissions, etc., see

e.g. WB, 2020) or setting incentives to implement energy-eﬃcient low-carbon technologies. The

assumed necessary carbon price to achieve Paris-compliant emission reductions varies, and de-

pends, amongst others, on assumptions on the parallel implementation of other climate policies.

For example, the IMF - assuming parallel implementation of green supply policies - calibrates

carbon prices to reach up to 40USD per ton of CO2 in 2030, and up to 150USD per ton CO2

in 2050, depending on the country. Conversely, Stern and Stiglitz, discussing alternative ap-

proaches to calculating the ”Social Cost of Carbon”, conclude that ”the numbers that are likely

to emerge would be more in the region of 100USD per ton by 2030” (Stern and Stiglitz, 2021)2.

In comparison, prices of EU emission allowances have increased to above 60EUR per ton CO2

recently3, with the EU Emissions Trading System (ETS) covering activities that account for

ca. 40% of the EU’s greenhouse gas emissions4. One important aspect of the implementation

of carbon pricing schemes is the potential misalignment across countries. This misalignment

could lead ﬁrms to move their production sites to countries where there are lower carbon pricing

1See e.g. https://news.un.org/en/story/2020/12/1078612
2The Social Cost of Carbon (SCC) refers to the ”economic cost caused by an additional ton of carbon dioxide
emissions or its equivalent”(e.g. Nordhaus, 2017), and ”can be used as a carbon tax, acting as a market price”
(Stern and Stiglitz, 2021).

3See https://ember-climate.org/data/carbon-price-viewer/
4The coverage of the EU ETS is currently limited to speciﬁc sectors.

In addition, a sizeable share of
ﬁrms/sectors is currently still subject to free allowances, implying that they do not have to purchase allowances
on the market.

ECB Working Paper Series No 2654 / March 20224schemes. However, in order to avoid such problem carbon border adjustment could be designed

(see, e.g. Parry, 2021).

Some ﬁrms may not be able to adapt their production processes and decrease their emissions

in alignment with overall necessary reductions. As a consequence, some non-ﬁnancial corpora-

tions (NFCs) might be at higher risk of default5. The risk resulting from such policies, but also

from technological or sentiment changes is commonly referred to as climate change transition

risk (e.g. NGFS, 2019; BCBS, 2021). Transition risk is argued to increase the longer climate

policies are delayed (e.g. NGFS, 2019), as the annual necessary reductions in greenhouse gas

emissions increase with each year in which climate action is delayed, and sudden and more strin-

gent policies might need to be implemented. If greenhouse gas emissions were reduced from 2020

onward, reductions of ca. 7.6% per year globally would be necessary to limit global warming

to 1.5◦C (UNEP, 2019) - a number comparable to the emission reductions estimated in 2020,

including the eﬀects of the Covid-19-related lockdown measures (Le Qu´er´e et al., 2020).

Transition risk is a potential threat for the ﬁnancial system (e.g. NGFS, 2019). Banks that are

highly exposed to NFCs that fail to adapt could suﬀer additional losses, which could exacerbate

pre-existing vulnerabilities and lead in the worst case to systemic stress. Such concerns are

ever more relevant when considering the ﬁnancial system is expected to be increasingly also

aﬀected by the physical consequences of climate change (physical risks). The monitoring of

climate-related ﬁnancial risks is therefore crucial, both for assessing the resilience of banks, and

the banking system as a whole.

Consequently, a number of studies have been published in recent years, attracting the at-

tention of both academics as well as central bank economists. One early example is provided

by Battiston et al. (2017) where network analysis is employed to examine the impact of the

introduction of climate policies onto the ﬁnancial system, yielding the conclusion that even

though exposure to climate policy relevant sectors are sizeable, climate policies would not have

adverse eﬀects if they are implemented timely. Building on this analysis, Roncoroni et al. (2019)

showed that for the Mexican ﬁnancial system (including investment funds), systemic losses are

contained (1%-2% of total assets in the Mexican ﬁnancial system) in mild scenarios while they

are found to be more severe (2.5%-4% of total assets) in a scenario where climate policies are

more stringent.

Recent work of central banks and supervisors included climate speciﬁc features into stress-

5If revenue streams do not grow accordingly.

ECB Working Paper Series No 2654 / March 20225testing or scenario analysis approaches, in order to measure the impact of climate risk on banks

balance sheets. The European Banking Authority has recently published its pilot exercise on

climate risk (EBA, 2021), highlighting the need for more disclosure and better data in order

to properly assess transition risk. French and Dutch central banks also started preliminary

stress-test exercises (see e.g. ACPR, 2019; Allen et al., 2020; DNB, 2018) envisaging the need

for further work to deepen the knowledge around the matter.

A report by the European Systemic Risk Board (ECB/ESRB, 2020) presented mixed evi-

dence on banks’ decarbonisation. Comparing emission intensities of large ﬁrms euro area banks

are exposed to between 2014 and 2017 suggests that some banks’ portfolios might have seen

decreases in their emission intensity, which might however be driven by companies reducing

their emissions (as opposed to banks redirecting their ﬁnancing towards greener corporations).

A similar analysis in the report suggests indeed banks seem to not have taken decisive action

in this context so far. The same report also presents a preliminary evaluation of the impact

of of two transition scenarios, namely an ”innovation shock” and ”delayed climate mitigating

policies”, on GDP, estimating that a delayed policy could give rise to loss in GDP as bad as 2%

in the short-term. A recent analysis jointly from ECB and ESRB (ECB/ESRB, 2021), more-

over, suggests that despite the exposure to ﬁrms and sectors highly exposed to transition risk

is overall manageable, pocket of vulnerabilities are still present and might exacerbate existing

risks especially from the credit portfolio.

Finally, the most recent ECB economy-wide stress climate stress test Alogoskouﬁs et al.

(2021) clearly show the beneﬁts for ﬁrms and banks to early adopt green policies. In fact, the

study shows how acting early could become a great advantage by outweighing the initial costs

due to increased eﬃciency and decreased energy prices. Not acting (or acting with signiﬁcant

delay) instead , would result in ever increasing risks and losses cause by physical events which

will become more frequent in an hot-house-world.

Given its unique and novel features, the importance of forward-looking approaches to measure

climate-related ﬁnancial risks is recognized (e.g. BCBS, 2021). Measurement approaches are

needed that are able to reﬂect the limited ability of historical data to act as a guide for the

future, and system interactions characterised by interconnectedness and non-linearity.

In this context, this present study contributes to the growing body of literature targeted

at measuring climate change transition risks for the ﬁnancial system. Using a banking sector

contagion model, this study estimates the impact that might stem from abruptly increasing

ECB Working Paper Series No 2654 / March 20226carbon prices, assessing the sensitivity of banking system losses to diﬀerent combinations of

carbon price changes and ﬁrm emission reduction strategies. The paper is structured as follows:

Section 2 describes the data used, Section 3 describes the modelling methodology and sensitivity

simulations performed for this study, and Section 4 discusses results from the sensitivity analysis.

Finally, Section 5 presents the conclusions and discusses policy implications of the ﬁndings.

ECB Working Paper Series No 2654 / March 202272 Data and methodology

The heterogeneity and wide range of climate related risks, both physical and transition, make

apparent the need for reﬁned granular borrower level exposure data. In particular, such hetero-

geneity speaks against the employment of country-sector level aggregates (Belloni et al., 2020),

which might average out signiﬁcant borrower-level risk exposures. Moreover, borrower-lender

information needs to be further enriched with climate data in order to allow for a thorough

quantiﬁcation of climate risks faced by ﬁnancial institutions.

This work exploits a quarterly granular dataset developed within the ECB which recon-

ciles information from diﬀerent data sources, including bilateral interbank exposures, exposures

to non-credit institutions, both ﬁnancial, non-ﬁnancial, and governmental, as well as banks’

holdings of securities (Montagna et al., 2020). Table 1 reports the ﬁnancial network summary

statistics.

Sector Nodes Edges Exposures [bne ] Securities [bne ]
CI
NFC
FC
HH
All

2623.6
2062.5
1019.1
21.8
7457.5

685.8
393.0
844.0
-
4086.6

10482
11569
6615
769
34787

1367
4125
3310
217
10354

(cid:104)LGD(cid:105)
0.321
0.406
0.423
0.292
0.340

(cid:104)PD(cid:105)
-
0.32
0.78
3.58
-

Table 1: Summary statistics by institutional sector: nodes are any consolidated entity present
in the system; edges refer to any bilateral exposure mapped between any two nodes; exposures,
reported in tn e , refer to any direct non-security exposure; the column ’Securities’ reports
instead all direct security exposures:
indirect exposures due to overlapping portfolios are not
reported here but are accounted for in the model; (cid:104)LGD(cid:105) and (cid:104)PD(cid:105) report the mean loss given
default and probability of default in each sector. Credit institutions do not receive a probability
of default as their dynamics is endogenously modelled. Data refers to reporting period 2019-Q4.

This dataset is further enriched with entity-level balance sheets, credit risk data, as well as

information on ﬁrm’s emissions. In order to quantify climate related risks, ﬁrms’ emissions are

employed to assess climate adjusted probabilities of default.

The analysis presented in this paper takes an entity-level view, requiring granular information

on banks’ equity and loan-book exposure, and ﬁrm-level emissions, as well as ﬁrms’ probabilities

of default, sales and total assets. For the former, supervisory statistics of banks’ Large Exposures

(LE) as well as Security Holdings Statistics by banking group (SHS-G) are used. Firm-level

ECB Working Paper Series No 2654 / March 20228emissions are retrieved from Urgentem6. Firms’ granular information on probabilities of default,

sales and total assets are taken from Moody’s and Orbis, respectively. Moreover, to compensate

for the lack of complete granular exposures (LE and SHS-G can only partially cover the total

amount of banks’ exposures), country-sectoral credit exposures are ﬁlled using FINREP.

2.1 Supervisory data

Though not speciﬁcally designed to assess climate-related risks, supervisory data can help assess

banks’ exposure to speciﬁc sectors/ﬁrms. Our analysis covers ca. 23.8 EUR trillions. of euro area

banks’ exposures, from roughly 1900 banks. This includes exposure to non-ﬁnancial corporations

as well as interbank exposures. Overall, exposure to ca. 5.9 EUR trillions to non-ﬁnancial

corporations is covered. As mentioned in the introduction, a share of granular banks’ exposures

comes from the Large Exposures (LE) reporting. Large Exposures covers exposures for amounts

above 300 (see (BCBS, 2014)) millions or exposures that account for more than 10% of bank

eligible capital before applying credit risk mitigations and exemptions (EBA, 2013).

In our

analysis LE accounts for ca. 7.4 EUR tn (or 34.8% of total exposures covered in the analysis)

of which more than a quarter of them is towards non-ﬁnancial corporations.

Interbank Real Economy

Nodes
Links
Exposures [bne ]

1367
10482
4309.42

Power-law exponent
Diameter

0.82
3.55

7435
18184
8647.90

0.81
2.92

Table 2: Network summary statistics for interbank and real economy. Data refers to 2019-Q4.

2.1.1 Securities Holdings Statistics

The second main data source of granular exposure used in this study is Securities Holding

Statistics by banking group (SHS-G). SHS-G provides granular information on a security-by-

security basis for euro-area banks for the following instrument types: debt securities, quoted

shares and investment funds shares. Individual securities data include ISIN and MFI codes which

allow us to map them with loans exposures ﬁrst and emissions data then. In the context of this

6Urgentem is an independent provider of carbon emission data; https://www.urgentem.net/

ECB Working Paper Series No 2654 / March 20229paper, securities are aggregated at holder-borrower level and information about instrument type,

maturity, and other instrument’s information are disregarded. Exposures through securities

amounts to ca. 4.1 EUR trillions of which less than 10% is towards NFCs.

2.2 Probabilities of default and LGDs

In order to assess the risk faced by credit institutions we leverage on ﬁrm-bank level data,

allowing for a granular estimation of default risks. Borrowers’ probabilities of default (henceforth

PDs) are retrieved from Moody’s Credit Edge7. Furthermore, LGDs are estimated at a granular

level from credit risk mitigation reporting 8 which incorporates information on the extent to which

exposures are collateralised, or guaranteed by a third party, or where the risk is hedged away by

means of credit derivatives. Probabilities of default refer to 2019 Q4, in order to disentangle the

eﬀects arising from the COVID-19 pandemic. Moreover, with the aim of comparing the impact

of a carbon tax and the COVID-19 eﬀect, probabilities of default from 2020 Q2 are also used in

the analysis.

2.3 Emissions

2.3.1 Emissions data

Oﬃcial emissions statistics (Eurostat) suggest that the highest contribution to overall direct

greenhouse gas emissions in the EU comes from ﬁrms in the sectors electricity/gas/steam, man-

ufacturing, agriculture and transportation. Within these sectors, the emissions are concentrated

in only a few sub-sectors, including crop and animal production for agriculture, and manufac-

turing of coke and reﬁned petroleum products, chemicals and chemical products, basic metals

and non-metallic mineral products. For transport, land transport has the highest contribution,

but emissions of air and water transport are also high. While high sector emissions often also

imply high emissions of individual ﬁrms, there may be large dispersion between ﬁrms within the

same sector (see, e.g. ECB/ESRB, 2020), requiring ﬁrm-level data as a proxy to assess ﬁrms’

and banks’ exposure to transition risks at entity level.

Firm-level emission reporting is still incomplete, inconsistent and insuﬃcient (ECB/ESRB,

2020). However, reasonable assumptions and methodologies can help ﬁlling data gaps9. The

7Missing information is ﬁlled by country-NACE4 level means.
8Credit risk mitigation is also retrieved from COREP.
9ECB/ESRB Project Team on climate risk monitoring, “Climate-related risk and ﬁnancial stability - Data

ECB Working Paper Series No 2654 / March 202210emission data used in this analysis includes reported data for ca. 1.000 of the total 4.000 ﬁrms

euro-area banks are exposed to through large exposure. For the remaining ca. 3.000 ﬁrms for

which data were not available or that could not be matched with emissions data, a country-

sectoral averaging was employed to ﬁll data gaps (see Table 3). Given the focus of this study

on the impacts of a carbon tax on non-ﬁnancial corporations, we focused on direct (“scope 1”),

and indirect energy-related (“scope 2”) emissions. Other indirect (”scope 3) emissions including

upstream and downstream emission categories such as transport, business trips or use of sold

products are not included.

n

inferred 3023
939
reported

Exposure amount (bn e) %
43.2
56.8

1011
1330

Table 3: Emissions coverage of non-ﬁnancial ﬁrms matched with LE and SHS-G

Moreover, one aspect often neglected when assessing ﬁrms’ emissions concerns ﬁrms relative

emissions eﬃciency, which might be largely diﬀerent across the sample (see Figure 1). Firms

might in fact be responsible of large amounts of GHG emissions, but what also matters is how

these amounts relate to the relative size and the revenues stream of the ﬁrms themselves. Also

in this respect there is high heterogeneity across countries and sectors (see, e.g. ECB/ESRB,

2020), which implies that also ﬁrms with similar levels of emissions might be able to withstand

very diﬀerently possible carbon price shocks.

Around 40% of large exposures towards non-ﬁnancial corporations (or 16% of total exposures

towards NFCs) of euro area banks are towards sectors that can be considered as climate policy

relevant, depending on the year. Here, sectors considered as climate policy relevant include

utilities, energy intensive, fossil fuel, transport and housing. This assessment is based on granular

information of ﬁrms’ economic activity, for which a relatively high coverage of euro area large

exposures can be achieved.

Diving into the relationship of exposures and emissions (see Figure 2) suggests that no

correlation can be found between the size of the exposure and the level of emissions. The lack of

correlation between these two measures highlights the importance of using granular information

when evaluating the impact of transition risks on ﬁrms and banks. This ﬁnding also emphasizes

the need to use data that are as granular as possible in order to better understand where pockets

supplement”, mimeo

ECB Working Paper Series No 2654 / March 202211Figure 1: Firms emission intensity; log-distribution. Emissions intensities are deﬁned as grams
of CO2e emissions over EUR sales.

Figure 2: Joint distributions of ﬁrms CO2e emissions and banks exposures.

of vulnerability are situated.

ECB Working Paper Series No 2654 / March 2022123 Modelling framework

A crucial challenge in the assessment of climate related risks comes from their forward-looking

non-linear nature (Bolton et al., 2020). Standard risk management practice relies on regression-

based approaches attempting to produce out-of-sample forecasts from historical data: while

this might be appropriate for small perturbations around an economy’s equilibrium, it becomes

inadequate and misleading in the face of large scale phase transitions such as those potentially

triggered by adverse climate impacts.

Nonetheless, forward-looking assessments are still possible and have started receiving in-

creasing attention in the past years. Here, we perform a sensitivity study, using NGFS scenarios

(IIASA, 2020) to obtain reference information about carbon price changes and emission reduc-

tions under diﬀerent climate policy assumptions. Assumptions on changes in carbon price and

ﬁrm emissions are then used to assess granular ﬁrm-level increases in corporates probabilities of

default, which are then translated into losses to the banking sector via a stochastic microstruc-

tural model of ﬁnancial contagion, yielding estimates of the loss distribution hitting the banking

sector conditional on the realisation of the climate scenarios.

A crucial feature of this approach is its ability to maintain a probabilistic approach while at

the same time conditioning on speciﬁc potential realisations of climate policy scenarios. This

is important as the mean and median behaviour of the system which are often taken as a

benchmark, might be by and large unaﬀected, with tail events becoming instead increasingly

likely to materialise and of greater magnitude.

3.1 Simulations

In order to assess the risk associated with abrupt transition shocks that might be transmitted

from the corporate sectors to the banking system we employ a micro-structural model of ﬁnancial

contagion built on granular euro area exposure data (see Appendix A for a detailed description

of the model). This class of models (Montagna and Kok, 2016; Craig and Von Peter, 2014;

Montagna et al., 2020) are characterised by their reliance on real reporting granular networks of

interbank exposures and securities portfolios, allowing for entity level disentangling of diﬀerent

sources of risk.

In particular, we account for four contagion channels: real economy credit

risk, interbank credit risk, liquidity risk, and market risk. The former accounts for credit risk

stemming from insolvent real economy counterparties, which can have repercussions on lenders’

ECB Working Paper Series No 2654 / March 202213balance sheets. Correlated real-economy insolvencies materialise stochastically through Monte

Carlo simulations based on counterparty level probabilities of default and are translated into

losses for corresponding credit institutions via entity-level exposures and associated losses given

default10.

In addition, an excessive materialisation of losses might also constitute a further

source of risk for both direct counterparties in the form of second-round contagion losses as well

as indirectly via overlapping-portfolio-mediated contagion (cf. Appendix A).

3.2 Climate adjusted probabilities of default

When assessing banking losses arising from transition risk the ﬁrm-level dimension acquires

crucial importance, since sector level shocks are known to overestimate overall losses (Belloni

et al., 2020). The reason is to be found in the large degree of heterogeneity in emission intensities,

whose distribution is characterised by fat tails and strong positive skew. Firm-level emission data

suggest a high degree of heterogeneity in emissions not only between sectors but also within,

with markedly power-law distributed tails. Consequently, a sectoral approach may fall short

of illustrating variability within a sector, making it necessary to take into account a granular

ﬁrm-level perspective when estimating the impact of transition risk on the ﬁnancial system.

The high degree of heterogeneity in counterparties’ credit risk as well as emission patterns,

makes a distributional analysis more desirable. For this reason, it is important to be able to map

emission intensities on a granular ﬁrm-by-ﬁrm level. In order to gauge the short term distress

on corporates facing new prices on carbon emissions, each ﬁrm’s credit risk is reassessed in a

Merton framework. More speciﬁcally, we assume that each ﬁrm would bear a fraction, β, of the

carbon tax. The carbon tax is applied on each ﬁrm independently of sector and country, solely

based on the level of emissions they produce in their production processes.

Adjusted probabilities of default are therefore computed at ﬁrm level by modelling each

ﬁrm’s asset value as a stochastic process in a Merton framework (Merton, 1974). In particular,

it is assumed that transition scenarios directly impact the value of a ﬁrm’s assets Ai, bringing

its climate adjusted value of assets A∗

i closer to the default point Li. One can therefore compute

climate-adjusted probabilities of default as:

P D∗

i = Φ

(cid:18) σi
2

−

1
σi

(cid:18)

µi + log

(cid:19)(cid:19)

.

A∗
i
Li

(1)

10A loss given default is applied which accounts for credit risk mitigation, as per COREP reporting information.

ECB Working Paper Series No 2654 / March 202214In this setting, ﬁrm’s i probability of default P Di(Ai, Li, µi, σi) is a decreasing function of its

liabilities and asset volatility, and an increasing function of assets. The sudden introduction of

a price on carbon T , can be thus thought of as a decline of ﬁrm’s value of assets, depending

on each ﬁrm’s emissions Ei, through an elasticity β < 1: the climate-adjusted value of assets

is therefore computed as: A∗

i = Ai − βT Ei. This, in turn, consistently results in increased

probability of defaults P D∗

i ≥ P Di

11.

3.3 Emission reduction strategies

Diﬀerent sets of simulations are performed in order to examine the sensitivity of the euro area

banking system to carbon price changes, considering diﬀerent ﬁrm emission reduction strate-

gies. The additional carbon cost born by the ﬁrms is proxied by the parameters β and T as

described in Section 3.2. The combined impact of diﬀerent levels of carbon price changes and

emission reductions can then be evaluated at representative levels of α = βT . The assumptions

underlying developments in carbon price and emissions are based on data obtained through

the NGFS scenario explorer hosted by IIASA (IIASA, 2020), using results for the EU (carbon

price, emissions) and global (temperature, 1.5◦C exceedance probability) from the integrated

assessment model REMIND-MAgPIE 1.7-3.0.12 The following sets of sensitivity simulations are

performed for this study:

• Constant emissions at 2018 levels, evaluated at levels of α corresponding to increases in

carbon price according to three diﬀerent policy pathways (1-3 in Fig. 3). These simulations

are representative for a situation in which the carbon price increases abruptly, without

ﬁrms being able to adjust their emissions.

• Reduced emissions according to three diﬀerent policy pathways (1-3 in Fig. 3), evaluated

for levels of α corresponding to an increase in carbon price consistent with the respective

policy pathway between diﬀerent points in time (Table 3.3).

Under the strictest policy assumption (1), the EU carbon price starts increasing sharply from

2020 onward according to NGFS scenarios, reaching ca. 180 US$ (2010)/t CO2 (or ca. 150e/t

11Notice this approach can also be directly applied to the KMV model by computing the adjusted distance
. This adjusted distance to default can then be mapped to a climate-adjusted EDF

log A∗
to default DD∗
i
Li
(expected default frequency) in the usual manner.

i = 1
σi

12The carbon price in these scenarios should be understood as a shadow carbon price, essentially reﬂecting the

overall policy stringency.

ECB Working Paper Series No 2654 / March 202215∆price2025 ∆price2035 ∆emissions2025 ∆emissions2035

(1)
(2)
(3)

immediate 1.5◦C
immediate 2◦C
delayed 2◦C

178
46
39

178
46
162

30%
15%
12%

81%
49%
50%

Table 4: Changes in carbon price in 2010 US$ per t CO2, under diﬀerent policy assumptions,
for diﬀerent points in time compared to ﬁve years earlier, and changes in emissions compared to
2020, according to NGFS (2020) and obtained through the NGFS scenario explorer hosted by
IIASA (IIASA, 2020). All scenarios rely on the REMIND-MAgPIE 1.7-3.0 integrated assessment
model.

CO2) in 2025 and a constant increase of ca. 180 US$ (2010)/t CO2 thereafter for every 5-year

period.

It should be noted that these prices correspond to the most stringent scenario with

only limited deployment of carbon dioxide removal technologies (also see NGFS, 2020). Steep

emission reductions are assumed to kick in as a consequence, down by 30% in 2025 (compared

to 2020), reaching net zero emissions in 2050 (see Figure 3). Global mean temperature increase

by 2100 would be limited to below 1.5◦C with a probability of ca. 75%.

Assuming a timely implementation of policies targeted at 2◦C (with limited deployment of

carbon dioxide removal technologies) also implies - according to NGFS scenarios - an increase

in carbon price and decrease in emissions from 2020 onwards, but less steep trajectories. Under

the assumption that the implementation of policies is delayed, the carbon price increases only

very little until 2030, with a sharp increase of ca. 160 US$ (2010)/t CO2 (or ca. 133e/t CO2)
in 2035 compared to 2030. In both cases, the probability of limiting global warming to 1.5◦C

by the end of the century is only ca. 40%, implying a higher risk from physical consequences of

climate change, including the risk to cross dangerous tipping points (IPCC, 2018).

ECB Working Paper Series No 2654 / March 202216Figure 3: Trajectories of carbon price, CO2 emissions, global mean temperature increase and
exceedance probability of 1.5◦C warming under the diﬀerent policy trajectories (1)-(3) considered
in this study, compared to current policies. Temperature increase in (c) is relative to 1850-1900,
and shaded areas denote the 25th-75th percentiles. Data source: NGFS (2020), model REMIND-
MAgPIE 1.7-3.0.

ECB Working Paper Series No 2654 / March 2022174 Results

4.1 Shock on PDs

Firms probabilities of default are adjusted to account for changes in carbon prices, as detailed in

Section 3. Therefore, for each emission reduction strategy deﬁned in Section 3.3, we derive the

associated adjusted probabilities of default. Figure 4 below presents the cumulative distributions

of PDs in each scenario.

Figure 4: Cumulative density distribution of probabilities of default by emission reduction strat-
egy (for an indicative α = 70).

4.2 Constant ﬁrm emissions

Under the assumption of ﬁrms’ emissions staying constant, banking system losses may be sizeable

with large changes in carbon price, and considerable tail risks are present in the system. On

average (median), an increase in carbon tax of 200e/t would lead to an increase of banking

system losses of ca. 10%, compared to the baseline (Fig. 6, Fig. 5 left panel, and Tab. B.2 in

the Appendix). While the impact on the center of the distribution would be relatively contained,

estimates on the impact on the tails of the loss distribution suggests rare events might acquire

more importance with increasing likelihood of large shocks materialising. Tail risks are high

with an increase in carbon price of 90e/t or more, with tail losses (expressed through the 99th

percentile of the loss distribution) increasing by ca. 10% with an increase in carbon price of

90e/t, and increasing by ca. 33% with an increase in carbon price of 200e/t (also see Tab. B.2

ECB Working Paper Series No 2654 / March 202218Figure 5: Statistics of banking system loss multipliers compared to a baseline scenario, assuming
constant emissions (0% emission reduction), and emission reductions of 15%, 30%, 50% and 80%,
depicted in the diﬀerent panels of the Figure. Colors indicate diﬀerent levels of α, with carbon
cost for ﬁrms α = β∗increase in carbon price, and β describing the pass-through of a carbon
price to ﬁrms.

in the Annex).

These results assume a full pass-through of the carbon price to ﬁrms and no further pass-

through to ﬁrms’ selling prices (β = 1 and α = β∗carbon price increase). With only a fraction

of the carbon price absorbed by ﬁrms (β < 1), sensitivity to the carbon price increase would

decrease proportionally, e.g. a carbon price of 200e/t and a pass-through of 50% would suggest

banking system losses to increase by ca. 2.8% on average, and ca. 12% in a tail scenario.

However, given only direct and indirect energy-related emissions (scope 1 and 2) are considered in

this calculation, and other upstream and downstream indirect emissions (scope 3) are excluded,

a price pass-through to ﬁrms of ca. 50% − 100%, depending on the sector, is a reasonable

assumption.

Compared to a scenario that reﬂects the impact of Covid-19 on the banking system in

2020, median losses would be comparable with a carbon price increase of ca. 150e/t, and larger

(4−7%) for carbon price increases of 200e/t and 250e/t. This implies that the expected impact

of a scenario in which the carbon price increases drastically suddenly, while ﬁrms are not able to

react, may have an impact that is comparable to the shock induced by Covid-19 in 2020. While

carbon price increases of this magnitude seem high compared to currently discussed prices (see

Section 1), such increases may be representative of a situation in which eﬀective climate policies

are delayed, and then implemented abruptly to limit the consequences of global warming.

ECB Working Paper Series No 2654 / March 202219Figure 6: Banking system loss distributions assuming constant emissions for diﬀerent levels of
α, with α = β∗increase in carbon price and β describing the pass-through of a carbon price to
ﬁrms. Assuming a full pass-through of the carbon price to ﬁrms (β = 1), α can be interpreted
as the cost sustained by ﬁrms for each tonne of carbon produced. Losses are compared to a
baseline situation. Distributions are based on 250 000 Monte Carlo simulations. Heights are
log-densities.

4.3 Assuming stylised ﬁrm emission reductions

Tail losses remain sizeable for high changes in carbon price and moderately ambitious levels

of emission reductions (Fig. 7). For example, with a reduction in ﬁrm emissions by 30%

and a carbon price increase of 150e/t (and β = 1), tail losses are estimated to reach ca. 14%,

compared to the baseline. This reduction in emissions corresponds to average estimated emission

reductions by 2025 compared to 2020 when pursuing policies to limit global warming to 1.5◦ by

2100 (see Fig. 3, blue line). For ﬁrm emission reductions of 50% and a carbon price increase of

150e/t, tail losses are estimated to only increase by ca. 7% compared to the baseline.

Assuming ambitious ﬁrm-level emission reductions of 50% or more compared to 2020 levels,

our results suggest contained banking system losses on average even for very high changes in

carbon price (Appendix B.1 and Fig. 5). With ﬁrm emission reductions of 50% and a carbon

ECB Working Paper Series No 2654 / March 202220price increase of 100e/t, average banking system losses are estimated to increase only by ca. 1%

compared to the baseline. This situation corresponds approximately to the estimated change in

emissions and necessary 5-year change in carbon price in 2035 compared to 2030, with policies

limiting global warming to 2◦ by 2100 (immediate policies, see Fig. 3, yellow line).

Median and tail banking system losses are sampled for diﬀerent steps of emission reductions,

as pictured in Fig. 8. The results suggest that already small decreases in emission reductions

can lead to a sizeable reduction in banking system losses compared to the baseline, implying

that already small reductions in ﬁrm-level emissions can lead to an important risk reduction.

For example, a decrease in ﬁrm-level emissions of 15% would, assuming a carbon price change

of 200e/t, lead to a banking system loss increase of ca. 6%, compared to 10% with constant

emissions. More detailed results and associated statistics can be found in Appendix B.1.

The results presented in this Section assume a uniform emission reduction by all ﬁrms in the

sample considered here. A further speciﬁcation of individual ﬁrm or sector emission trajectories

is beyond the scope of this sensitivity study, as it would require information on ﬁrm level emission

scenarios, ideally based on information disclosed at ﬁrm level (e.g. emissions reduction targets,

sustainability linked loans, etc.). However, an extension of this analysis is needed to explore

whether diﬀerent pockets of risk could emerge for the euro area banking system if entire sectors,

or groups of ﬁrms fail to ambitiously reduce their emissions.

ECB Working Paper Series No 2654 / March 202221Figure 7: Banking system loss distributions for moderately ambitious emission reductions (−30%
compared to 2020) and diﬀerent levels of α, with α = β × carbon price and β describing the
pass-through of a carbon price to ﬁrms. Assuming a full pass-through of the carbon price to
ﬁrms (β = 1), α can be interpreted as the carbon cost sustained by ﬁrms. Losses are compared
to a baseline situation. Distributions are based on 250 000 Monte Carlo simulations. Heights
are log-densities.

Figure 8: Increase in banking system losses declines with increase in ﬁrm emission reductions;
median banking system losses (LHS) and tail losses (95th to 99th percentiles, RHS).

ECB Working Paper Series No 2654 / March 2022225 Conclusions

The study presented here uses a network contagion model to assess the sensitivity of the euro

area banking system to changes in carbon price. Changes in carbon price applied for ﬁrms’ direct

(scope 1) and energy-related (scope 2) greenhouse gas emissions are translated into increased real

economy probabilities of default which in turn result into additional losses on lenders’ balance

sheets. This allows to probe the ﬁnancial stability implications of the introduction of diﬀerent

policies while conditioning on diﬀerent emission reduction scenarios. The sensitivity of results

to diﬀerent stylised levels of ﬁrm emission reductions is also tested.

Results suggest the banking system may be facing substantial risks only with high and

abrupt changes in carbon price, if ﬁrms do not reduce their emissions accordingly. If delayed

policy action makes an abrupt introduction of very high changes in carbon prices (>150 EUR/t)

necessary, the banking system may be subject to a shock comparable to that induced by the

Covid-19 pandemic in 2020.

This study further ﬁnds that high changes in carbon prices might still entail tail risks for the

banking system if ﬁrms reduce emissions only lightly. In turn, large changes in carbon prices

together with ambitious, Paris-consistent emission reductions at ﬁrm level across ﬁrms are likely

to not lead to systemic stress for the banking system.

These results are achieved under the assumption of a full pass-through of a carbon price

change to ﬁrms13, and homogeneous emission reductions across all ﬁrms, and therefore represent

an upper limit of the impact of increases in shadow carbon price. Further research is needed to

study what share of carbon price increases would be absorbed by ﬁrms and how their balance

sheets would be impacted, depending on their emission reduction strategies. Future studies

should also investigate how more heterogeneous emission reductions, or a carbon price only

applied to speciﬁc ﬁrms/sectors, may propagate to the banking system, e.g. assuming impacts

only in speciﬁc industrial sectors or ﬁrms. In addition, more comprehensive scenario analyses

are needed to consider a broader range of potential transition shocks and transmission channels

to the ﬁnancial system. Furthermore, such studies will beneﬁt from increased eﬀorts to improve

ﬁrm-level disclosure of their carbon emissions including both direct and indirect emissions, as

well as the disclosure of (credible) forward-looking ﬁrm strategies to reduce emissions.

Overall, results presented here suggest that in order to shield themselves from losses, banks

13Though the results discussed here are interpreted for a full pass-through of a carbon price change to ﬁrms,

they can also be interpreted for a limited pass-through.

ECB Working Paper Series No 2654 / March 202223should assess lending to ﬁrms that are not following ambitious emission reduction strategies.

Importantly, the results presented here underline the importance of banks’ knowledge of their

clients’ carbon footprints and emission reduction strategies. Consequently, policy measures are

needed to foster bank and ﬁrm disclosure of both direct and indirect emissions as well as the

disclosure of veriﬁable strategies to reduce emissions. In addition, prudential measures may be

necessary to prevent the built-up of banking system losses or pockets of risks through bank

exposures to ﬁrms that are not able to adapt their business models to a strategy consistent with

meeting the goals of the Paris agreement.

Finally, even though the most ambitious policy measures and emission reductions may not

completely prevent the materialization of banking system losses, these losses seem to be limited

compared to the physical consequences of climate change documented in the literature: global

consequences of unmitigated climate change may trigger currently unforeseen consequences,

ranging from climate system changes by crossing climate tipping points, to strongly decreasing

the area of habitable places on Earth, threatening lives and the economic and political stability

of societies.

ECB Working Paper Series No 2654 / March 202224A Financial system dynamics

Consider a set of B banks, characterised by the vectors K of banks’ capitals, and cash holdings C.

Moreover consider a set of E real economy entities (borrowers), and a set S securities. The ﬁnan-

cial system is the multilayer network deﬁned by the collection M = ({B}, {S}, {E}, L, S, E, F),

where L, S ∈ RB×B are the weighted adjacency matrices of unsecured short and long term cross-

bank exposures, E ∈ RB×E the weighted adjacency matrix of unsecured banks to real economy

exposures, and F ∈ RB×S the banks’ portfolios holdings. Banks are subject to both solvency

as well as liquidity constraints. A solvency default threshold DK
j

is deﬁned for each institution

as the level of minimum capital requirements plus AT1/T2; in addition, a solvency distress

threshold T K

j

corresponding to the combined buﬀer requirements is also introduced. Similarly,

constraints on liquidity are also accounted for through liquidity default thresholds DC

j = 0, and

liquidity distress thresholds T C
j

constructed based on individual institutions’ liquidity coverage

ratios. Each bank is therefore further characterised by a trichotomic state encoded in the status

vector s ∈ RB: healthy (sj = 0 when Kj > T K
j
DK

and Cj > T C
j ), or defaulted (sj = 2 when either Kj < DK

j < Kj < T K
j

j < Cj < T C

or DC

j ), distressed (sj = 1 when either

j or Cj < DC

j ).

The system dynamics accounts for three mechanisms of contagion, each modelling a speciﬁc

class of risk, and each contributing to the ampliﬁcation and worsening the eﬀects of the others,

so that the contagion stemming from each one individually is not simply additive. This is a

particularly important feature for a realistic modelling of contagion unfolding. The classes of

risk considered, whose modelling is described below, are credit, liquidity, and market risk. While

modelling of the ﬁrst is a mechanical balance sheet contagion mechanism, liquidity and market

mechanics involve the search for an equilibrium clearing vector among all market participants in

the spirit of (Eisenberg and Noe, 2001). These three mechanisms are iterated until convergence

to a steady state in which no more contagion spreads through the system.

Real Economy Credit Risk

The banking system’s exposures to real economy entities provide a source of exogenous risk,

which can translate, through cascade eﬀects, into ampliﬁed losses for banks.

In particular,

the bipartite topological relation between the banking and real economy sector is crucial in

determining how contagion spreads. Yet another crucial role is played by the distribution of

probabilities of default P Dj associated with each of the E ﬁrms.

In order to capture such

ECB Working Paper Series No 2654 / March 202225features, the dynamics is initiated via multiple stochastic realisations of defaults.

More speciﬁcally, we seek to sample multivariate Bernoulli vector of defaults dE ∈ RE with
marginal probabilities P Dj and correlation structure deﬁned by a correlation matrix Σ 14.

For each realisation of the Bernoulli vector dE , one ﬁnds a corresponding realisation of losses

(cid:96)0 = E · dE for the banking system. Note that security exposures are also accounted for in E.

Such a stochastic approach allows to perform Monte Carlo simulations of diﬀerent states of the

system, hence permitting to study distributional properties of contagion.

One among the possible approaches to sampling correlated multivariate Bernoulli vectors

consists in thresholding a multivariate normal distribution with the appropriate correlation

structure. Denoting by z(p) the pth quantile of the standard normal distribution, a multivariate

Bernoulli vector can be sampled as

(dE )j =



0


1

if Zj > z(P Dj)

if Zj ≤ z(P Dj)

(2)

where Z ∼ N (0, ¯Σ). Crucially, the correlation matrix ¯Σ is not the desired correlation matrix,
which is instead denoted by Σ. In order to infer ¯Σ, one should consider that

Σjk = corr[(dE )j, (dE )k] =

=

=

=

=

cov[(dE )j, (dE )k]
(cid:112)P DjP Dk(1 − P Dj)(1 − P Dk)
P ((dE )j = (dE )k = 1) − P DjP Dk
(cid:112)P DjP Dk(1 − P Dj)(1 − P Dk)
P (Zj ≤ z(P Dj), Zk ≤ z(P Dk)) − P DjP Dk
(cid:112)P DjP Dk(1 − P Dj)(1 − P Dk)

Φ[z(P Dj), z(P Dk), ¯Σjk] − P DjP Dk
(cid:112)P DjP Dk(1 − P Dj)(1 − P Dk)

(3)

where Φ[x, y, σ] denotes the standard bivariate normal distribution. This can be solved elemen-
twise for ¯Σ.

14The correlation matrix Σ is proxied by correlation of CDS spreads at country-sector level.

ECB Working Paper Series No 2654 / March 202226Interbank Credit Risk

Within the long term layer of interbank credit exposures, described by the weighted adjacency

matrix L of unsecured loans, contagion arises from the insolvency of credit institutions.

In

particular, the dynamics is initiated by a vector of losses (cid:96)0 ∈ RB which is transmitted to each

individual institution, resulting in a reduction of the vector of capitals. This starts the contagion

mechanism by inducing distresses and/or defaults within the system. Upon updating the vector

s, the realisation of credit risk coming from banks initially defaulting materialises into a new

vector of losses (cid:96) = L · dB, where dB ∈ RB is the vector of banks in default with elements

(dB)j = θ[sj − 1] (θ being the discrete Heaviside function). Thereby, the capitals are updated

as

Kt+1 = Kt − (cid:96),

(4)

and the vector s is updated accordingly. Following solvency contagion, the system undergoes

further dynamics on the liquidity and market layers, which might lead to further cases of insol-

vency. As mentioned above, the credit risk mechanics is then reiterated followed once again by

the other mechanisms, until the system reaches a steady state.

Liquidity Risk

Following the unfolding of credit contagion, banks might ﬁnd themselves in a state of distresses,

leading to possible further turmoils on the liquidity side (Montagna et al., 2020). In particular,

the liquidity contagion mechanism is triggered by preemptive withdrawals from defaulted and

distressed banks (Minca and Sulem, 2014), as well as liquidity hoardings from the latters (Covi

et al., 2021).

Here we do not account for solvency losses in the short term market, assuming that coun-

terparties of a FOLTF institution have suﬃcient time to withdraw their positions, given that

the time scales of default tend to be longer than the average maturity in this market segment.

Instead, we allow banks to satisfy their liquidity needs via pro rata interbank withdrawals –

accounted for by the matrix W ∈ RB×B – constrained on their short term assets availability,

as well as on the needs of all other market participants. In order to do so, each institution’s

liquidity shortfall must be a function of the amount of short term funding each other bank is

ECB Working Paper Series No 2654 / March 202227withdrawing, and can thus be written as


T C

i − Ci +

LS

i =



+

Wji − Wij



.

(cid:88)

j

(5)

Consequently, the (residual) short term assets will also be determined in function of such with-

drawing as AR

i = (cid:80)

j Sij − Wij, and each bank will seek to withdraw a fraction

χi =

LS
i
AR
i

∧ 1

(6)

of its short term assets15. Searching for the optimal amount of withdrawing is then equivalent

to ﬁnding a ﬁxed-point for W and χ, which corresponds to the system’s equilibrium (whose

existence is guaranteed by the constraints imposed, making χ bounded and monotonic).

Due to the non-linearity of the iterator map, one cannot ﬁnd a closed form expression for

such an equilibrium. Therefore, an explicit computation of the iterator steps is required, leading

to an algorithmic procedure which can be loosely interpreted as the unfolding of a liquidity crisis

over the course of a short period of time. As mentioned, such an unfolding is triggered by the

preemptive withdrawals from defaulted and distressed banks (status sj = 1 or 2), which in turn

withdraw their short term holdings as well. Thereby, the initial matrix of withdrawals can be

written as

Wij =




Sij,



0,

if si > 0, or sj > 0,

otherwise.

(7)

Through this mechanism, the system might generate liquidity shortages, so that each institution

will seek to obtain additional liquidity LS

i . Here the assumption that each bank will then cover

such additional liquidity needs by further withdrawing pro rata, according to its needs and

proportionally to the size of each exposure, is made. In particular, a bank in short of liquidity

(LS

i > 0) and with positive residual assets AR
15Here we employ the by now standard in the ﬁeld notation (Eisenberg and Noe, 2001) for the element-wise

i , will withdraw a fraction LS

i of its assets from

i /AR

minimum and maximum operators: (x ∧ y)i = min{xi, yi}, (x ∨ y)i = max{xi, yi} for x, y ∈ Rn .

ECB Working Paper Series No 2654 / March 202228the short term market. That is, the extra withdrawal is

LS
i
AR
i

(Sij − Wij),

if AR

i > LS

i > 0,

W e

ij =

Sij − Wij,






0,

if LS

i > AR

i > 0,

otherwise.

(8)

This amount is added to the withdrawal matrix so that Wτ +1 = Wτ + W e

τ , where τ labels the

integer steps of the iterator before convergence. A new value for the extra withdrawals is then

computed until convergence of W to equilibrium, signalled by the convergence of the matrix of

additional withdrawals to zero: W e

ij = 0, ∀i, j.

Notice that to get to such a ﬁxed point equilibrium state, might not necessarily imply that

each bank has fulﬁlled its liquidity needs. More speciﬁcally, this would occur when the entirety

of the short term holdings is not suﬃcient to cover the liquidity needs of one institution. The

liquidity positions of all institutions are thus updated, but those in need of additional cash are

given the opportunity to raise more through deleveraging: any outstanding liquidity shortage

will thus need to be dealt with through the liquidation/decumulation of securities.

Market Risk

Within a network of ﬁnancial institutions with overlapping portfolios, indirect exposures arising

from investments in common assets have the potential to pose signiﬁcant risk in times of distress,

even for institutions with no direct linkages (Cont and Schaanning, 2019). The price-mediated

contagion stemming from the depreciation of assets liquidated by deleveraging institutions, leads

to strong ampliﬁcation mechanisms and feedback loops which contribute to aggravate the sys-

temic distress, stimulating further system-wide losses.

While such deleveraging mechanisms can in general be triggered by any kind of portfolios

devaluations including exogenous shocks, here we consider only the case of endogenously gener-

ated depreciations of the banks’ portfolios. In particular, the sale of securities is initiated either

by banks in default, or by institutions with residual liquidity shortages LS

i > 0. Because of the

depreciation of liquidated assets, each agent in the system must solve an optimisation problem

subject to the liquidity needs of all other market participants. Moreover, following portfolios

depreciations, more market players might join the sale of assets, giving rise to cascade events.

Denoting by F ∈ RB×S the decumulation matrix, and by p ∈ RS a normalised vector of

ECB Working Paper Series No 2654 / March 202229prices, the residual liquidity needs can now be written as


T C

i − Ci −

LS

i =



+

Fijpj



.

(cid:88)

j

(9)

The liquidity each institution can raise from liquidation of its marked to market assets AM =

(F − F) · p is clearly constrained by the amount it initially holds, as well as by the equilibrium
price vector, determined through the price impact function P(p, ∆), where ∆ = (cid:80)

i Fij is the
vector of volumes sold of each individual security. Each bank in need of liquidity will then seek
to sell a pro rata fraction χi = LS
i
AM
i
by the optimal matrix of decumulation F and portfolio liquidation vector χ.

∧ 1 of its assets. The system equilibrium is here represented

Once again, an algorithmic approach must be taken in order to ﬁnd such an equilibrium. At

any point in time, the value of the portfolio of assets each bank disposes of is F · pτ , with p0 a

vector of prices with each element normalised to unity at time zero. Each step of the iterator,

consists here in computing a new decumulation matrix according to

Fij =




Fij,

if si = 2, or LS

i ≥ F · p,



LS
F·p Fij, otherwise.
i

The amount of security j sold is thus ∆j = (cid:80)B

i=1 Fij, and the prices are updated as

pτ +1 = P (pτ , ∆) .

(10)

(11)

Following the price level reduction in the market layer, the liquidity requirements of some market

participants might not be any longer satisﬁed: this will lead to further liquidation of assets

and consequent depreciations. Convergence of the decumulation matrix is here signalled by

convergence of the price vector, or equivalently of the vector ∆. Once the equilibrium is achieved,
the security holdings are updated to F − F, as well as the cash holdings as Ci + (cid:80)

j Fijpj.
Most importantly, the risk from indirect exposures materialises in the form of a vector of losses

F · (p0 − p) which is then deducted from the banks’ capitals. This mechanism leads to further

credit risk contagion, possibly leading to further distress in the system, until convergence to

steady state.

A ﬁnal note is in order with regards to the price impact function. One standard approach in

ECB Working Paper Series No 2654 / March 202230modelling market slippage is to make the assumptions – justiﬁable under Kyle’s model (Kyle,

1985) – that the impact on price of a given transaction is linear in the traded volume, and that

its eﬀects are permanent. That is to say PK(p, ∆) = p ± λ∆, where 1/λ is a measure of market

depth, and the sign of the price impact is determined by whether the transaction is sell or buy

initiated. Finally, price impact parameters are calibrated from market data as in (Fukker et al.,

2021).

B Results details

B.1 Loss distributions

The set of ﬁgures below shows in a more detailed manner banking system losses distributions

across each α and each emissions reduction strategy. More information on emissions reduction

strategies and the meaning of α can be found in the main text in Section 3.

ECB Working Paper Series No 2654 / March 202231(a) α = 10

(b) α = 20

(c) α = 30

(d) α = 40

(e) α = 50

(f) α = 60

(g) α = 70

(h) α = 80

(i) α = 90

(j) α = 100

(k) α = 150

(l) α = 200

(m) α = 250

(n) all

Figure 9: No emissions reduction strategy implemented

ECB Working Paper Series No 2654 / March 202232(a) α = 10

(b) α = 20

(c) α = 30

(d) α = 40

(e) α = 50

(f) α = 60

(g) α = 70

(h) α = 80

(i) α = 90

(j) α = 100

(k) α = 150

(l) α = 200

(m) α = 250

(n) all

Figure 10: Emissions reduction strategy of 15%

ECB Working Paper Series No 2654 / March 202233(a) α = 10

(b) α = 20

(c) α = 30

(d) α = 40

(e) α = 50

(f) α = 60

(g) α = 70

(h) α = 80

(i) α = 90

(j) α = 100

(k) α = 150

(l) α = 200

(m) α = 250

(n) all

Figure 11: Emissions reduction strategy of 30%

ECB Working Paper Series No 2654 / March 202234(a) α = 10

(b) α = 20

(c) α = 30

(d) α = 40

(e) α = 50

(f) α = 60

(g) α = 70

(h) α = 80

(i) α = 90

(j) α = 100

(k) α = 150

(l) α = 200

(m) α = 250

(n) all

Figure 12: Emissions reduction strategy of 50%

ECB Working Paper Series No 2654 / March 202235(a) α = 10

(b) α = 20

(c) α = 30

(d) α = 40

(e) α = 50

(f) α = 60

(g) α = 70

(h) α = 80

(i) α = 90

(j) α = 100

(k) α = 150

(l) α = 200

(m) α = 250

(n) all

Figure 13: Emissions reduction strategy of 81%

ECB Working Paper Series No 2654 / March 202236B.2 Loss statistics

α
10
20
30
40
50
60
70
80
90
100
150
200
250

constant emissions
0.35
0.64
0.72
0.83
1.01
1.32
1.73
2.02
2.39
2.83
6.66
10.15
13.55

15% reduction 30% reduction 50% reduction 80% reduction

0.26
0.59
0.68
0.76
0.87
1.03
1.29
1.73
1.84
2.18
4.79
8.08
10.92

0.29
0.50
0.65
0.71
0.77
0.87
0.99
1.18
1.47
1.73
3.09
5.90
8.49

0.20
0.34
0.53
0.63
0.68
0.72
0.77
0.83
0.91
1.00
1.79
2.80
4.55

0.23
0.22
0.24
0.27
0.32
0.39
0.46
0.53
0.58
0.62
0.70
0.80
0.94

Table 5: Increase in median losses with diﬀerent levels of alpha and diﬀerent assumptions on
ﬁrm emission reductions, compared to 2020 (in percent).

α
10
20
30
40
50
60
70
80
90
100
150
200
250

constant emissions
0.81
1.61
2.40
3.34
4.70
5.89
7.30
8.54
10.46
12.67
24.20
33.32
42.22

15% reduction 30% reduction 50% reduction 80% reduction

0.63
1.46
2.02
2.75
3.51
4.82
5.79
7.06
8.02
9.34
19.32
27.73
35.24

0.44
1.17
1.70
2.22
2.84
3.50
4.52
5.66
6.41
7.32
13.89
22.40
28.89

0.33
0.78
1.26
1.61
1.99
2.33
2.78
3.28
3.88
4.66
7.81
12.56
18.55

0.21
0.25
0.36
0.46
0.72
0.89
1.07
1.26
1.46
1.50
2.20
3.06
4.09

Table 6:
assumptions on ﬁrm emission reductions, compared to 2020 (in percent).

Increase in tail losses (99th percentile) with diﬀerent levels of alpha and diﬀerent

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ECB Working Paper Series No 2654 / March 202241Acknowledgements 

We are grateful to Stephan Fahr and Paul Hiebert for helpful comments and discussions. We also thank Rafel Moyà-Porcel and Petya 
Radulova for their contributions during the earlier stage of this work. 

Marco Belloni 
European Investment Bank, Luxembourg, Luxembourg; email: m.belloni@eib.org 

Friderike Kuik 
European Central Bank, Frankfurt am Main, Germany; email: friderike.kuik@ecb.europa.eu 

Luca Mingarelli 
European Central Bank, Frankfurt am Main, Germany; email: luca.mingarelli@ecb.europa.eu 

© European Central Bank, 2022 

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