Stress testing with multi-faceted liquidity : the central bank collateral framework as a financial stability tool.
Date: 2023-05-10
Institutions: European Central Bank
Subjects: European Central Bank, central bank, financial solvency, financial stability, financial stress test, financing, money-market liquidity

Angelo Cuzzola, Claudio Barbieri, 
Ulrich Bindseil 

Working Paper Series 

Stress testing with multi-faceted 
liquidity: the central bank collateral 
framework as a financial stability tool 

No 2814 

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

The paper studies the central bank collateral framework and its impact on banks’ liquidity under an
adverse stress test scenario. We construct a stress test model that accounts for a granular and multi-
faceted representation of the liquidity of marketable and non-marketable assets. In particular, the
model analyses banks’ strategic decisions to mobilise assets through four funding channels: unsecured
loans, asset sales, private repurchase agreements, or Central Bank lending. We test three scenarios:
the EBA regulatory stress test exercise, a shock to Russia and the Eastern European countries, and
a shock to the Southern European countries. Results show that illiquidity can trigger insolvency
and that liquidity adjustment can last significantly after the initial shock. We find evidence of a
threshold in the benefits of expanding the collateral framework and highlight the heterogeneous
effects across different jurisdictions and financial institutions. We find that bank equity losses are
reduced in aggregate up to 17% at the tail of the loss distribution and on average by around 5%
when financial institutions can rely on the collateral framework channel.

Keywords: Central Bank Collateral Framework, Lender-Of-Last Resort, Asset liquidity, Collateral,
Stress test

JEL classification: C63, E52, G01, G28

ECB Working Paper Series No 28141Non-technical summary

In times of distress, refinancing operations play a fundamental role in monetary policy
transmission, granting market stabilisation and providing ample liquidity to finan-
cial intermediaries, eventually supporting the credit provision to the real sectors.1
Therefore, the modelling of refinancing operations should not only consider the set-
tled interest rate, the issued volumes and the auction design. Since credit to financial
institutions is provided against collateral, the features of the required guarantees are
also a key element to consider.

The Central Bank’s collateral framework (CBCF) is the system of rules through
which central banks define the characteristics of eligible collateral. The regulation in-
cludes fundamental information on the criteria for collateral eligibility, the methodol-
ogy used to evaluate assets, and the computation of the haircuts applied to assets after
the evaluation. The accepted assets and transactions conditions significantly modify
the levels of liquidity provision to the financial system, eventually affecting the size of
banks’ liquidity buffers relative to their short-term liabilities2. The CBCF, therefore,
plays a primary role in shaping the maturity mismatch between short-term debt and
medium/long-term loans. Therefore, a granular representation of balance sheet char-
acteristics becomes more relevant as including or excluding a particular class of assets
in the collateral framework (or changing the associated haircuts) radically transforms
the liquidity landscape and access to funding.

The present analysis extends previous studies, which attempt to provide a quantita-
tive setting to inform the debate on the appropriateness of the CBCF scope (Ashcraft
et al., 2011; Bindseil et al., 2017b; Bindseil and Lanari, 2022). We add in particular to
the stream of models that design explicitly the features of the CBCF coupled with a
sensible representation of the regulated financial systems and its main building blocks,
i.e. (i) the assets variety in terms of scope of the investments or liquidity, (ii) the
heterogeneity of the banks operating in the markets with diverse business models, and
(iii) the different strategies to deal with financial shocks and market distress.

Building on Cont and Schaanning (2017a, 2019) and Cont et al. (2020), we intro-
duce a model where shocks to assets values induce endogenous liquidity shortfalls to
which banks respond using four diverse financing sources: asset sales, unsecured credit,
repo credit or Central Bank credit. Such an extension defines multiple interactions in
the solvency-liquidity landscape, leading to the amplification of exogenous shocks.

We propose two applications of the model. The first is based on a simulated finan-

1 See e.g. Hutchinson et al. (2020); Lane (2020) for the case of the Eurosystem during the COVID19

crisis.

2 On this regard, recall that insufficient buffers relative to short-term liabilities have been pointed
to be a trigger of the GFC, and one of the primary causes of an (at least temporarily) excessive
reliance on Central Bank funding (BCBS, 2013).

ECB Working Paper Series No 28142cial system with banks and investors/depositors, where balance sheets are simulated
in line with the empirical analysis by Farnè and Vouldis (2021). Next, we present an
application on empirical data using the Financial Information Reporting (FINREP)
framework, which includes information on balance sheets, income statements and eq-
uity, financial assets and liabilities at the bank level, and AnaCredit, which integrates
the granularity of exposures to non-financial corporations. We test the effect of a col-
lateral framework expansion on the financial system’s exposure to bank-specific and
systemic losses. Then we compare the outcomes of stress tests in two cases: one
in which banks have access to multiple channels and, in particular, to credit-upon-
collateral to deal with liquidity and asset values shock, the other in which the only
available strategy is to sell assets at endogenously determined market prices. We find,
in particular, that:

• while homogeneous expansions of the collateral framework have a significant im-
pact on equity losses, the benefits do not increase linearly with the magnitude of
the widening yet become stationary after a certain threshold in haircut reduction;

• bank equity losses are reduced in aggregate up to 17% at the tail of the loss
distribution and on average by around 5% when financial institutions can rely
on the collateral framework channel

The collateral framework of the ECB has been the object of a lively debate involving
central bankers and practitioners discussing the appropriateness of its scope and the
principles and objectives of monetary authorities (Calomiris et al., 2016; Nyborg, 2016;
Bindseil and Laeven, 2017). To inform the debate, we find evidence of the collateral
framework’s heterogeneous and non-linear risk-mitigating effects for both the simulated
and the empirical applications.

There are several ways to extend the present study. For instance, while we model
constant haircuts for assets and the repo market, haircuts might change during a crisis.
Similarly, we obtain conservative estimates for the shocks mediated by price contagion
since the market impact of asset sales is modelled through a linear pricing function.
However, non-linearity could be tested to fit closer the price reactions in periods of
distress (see e.g. section 3.2 in Cont and Schaanning, 2017a, for a discussion). Lastly,
the analysis focuses on indirect contagion entailed by the overlap of portfolio exposures
between banks and does not analyse possible second-round effects due to bank defaults.
We discuss such restrictions throughout the paper and leave possible extensions to
further research.

ECB Working Paper Series No 281431

Introduction

1.1 Relevance of the collateral framework in stress tests

The Global Financial Crisis (GFC) of 2007-08 highlighted the importance of bank in-
termediation in maintaining the pressure on the financial system at sustainable levels
in times of distress. During the last decades, to support the financial institutions in
the achievement of their intermediation outcomes, Central Banks fine-tuned conven-
tional monetary policy, introduced unconventional measures, and complemented their
policy toolkit with liquidity regulations and capital standards enforced by supervisory
authorities.

More recently, the global macroeconomic shock following the outbreak of the Covid
19 pandemic has put through the winger the complete set of precautionary measures
and their effectiveness in mitigating financial distress: in a context of severe disloca-
tion of the financial markets (Zhang et al., 2020; Albulescu, 2021; Gubareva, 2021),
involving even the most liquid segments (Ziemba, 2020; Zaremba et al., 2021; Kargar
et al., 2021; Zaremba et al., 2022), Central Banks across the world undertook actions
that outpaced the previous responses to the GFC both in scope and size aiming at
maintaining continuous access to liquidity and favourable credit conditions to the pri-
vate sector (English et al., 2021; Cantú et al., 2021). Flourishing literature studied
both theoretically and empirically the role of monetary channels, trying to measure
their impact once taken singularly, see e.g. Altavilla et al. (2014) Levin and Sinha
(2020), Moessner and de Haan (2022), Altavilla et al. (2015) and Aguilar et al. (2020),
or assessing their joint effectiveness (Curdia and Woodford, 2011; Popoyan et al., 2017;
Altavilla et al., 2019; Bernanke, 2020; Wei and Han, 2021) with a particular focus on
non-standard (or unconventional) policies (Altavilla and Giannone, 2017; Bhar and
Malliaris, 2021).

Despite adopting diverse methodologies, the extant literature does not always em-
phasise certain aspects of refinancing operations. Such policies have proven to be
fundamental for monetary policy transmission, granting market stabilisation and pro-
viding ample liquidity to financial intermediaries, eventually supporting the credit
provision to the real sectors (see e.g. Hutchinson et al., 2020; Lane, 2020, for the case
of the Eurosystem during the Covid-19 crisis)). When considering refinancing opera-
tions, especially, their modelling should not only consider the settled interest rate, the
volumes effectively issued and the auction design. Since credit to financial institutions
is provided against collateral, the features of the required guarantees are also a key
element to consider. The Central Bank’s collateral framework (CBCF) is the system
of rules through which central banks define the characteristics of eligible collateral.3.

3 See e.g. Chailloux et al. (2008) for a general review.

ECB Working Paper Series No 28144The rules include fundamental information on the criteria for collateral eligibility, the
methodology used to evaluate assets, and the computation of the haircuts applied to
assets after the evaluation4.

The assets accepted and the conditions of the transactions significantly modify
the levels of liquidity provision to the financial system, eventually affecting the size
of banks’ liquidity buffers relative to their short-term liabilities5.
Indeed, while ac-
tively contributing to the maturity transformation in financial markets, banks keep
unbalanced the ratio between short-term debt and medium/long-term loans to the
real economy. Such a mismatch poses a trade-off between the efficiency of the banking
system in delivering maturity transformation and financial stability.6 The degree of
such a maturity mismatch links directly to financial stability and the composition of
the long-term investments at both aggregate and bank-specific levels.

Within this framework, CBCFs become more relevant as they interact with the
granular characteristics of the balance sheets of the financial institutions populating
the banking system.
Including or not a particular class of assets in the collateral
framework (or changing the associated haircuts) radically transforms the liquidity
landscape and the access to funding sources of financial intermediaries. For this reason,
the definition and calibration of the collateral frameworks are among the most complex
and economically significant elements of monetary policy implementation (Bindseil
et al., 2017a) and played a relevant role in the last decade and during the COVID-
19 crisis (see the scope and the amount of the used collateral as in Fig. 1). Non-
coincidentally, the collateral framework of the ECB has been the object of a lively
debate involving central bankers and practitioners discussing the appropriateness of
its scope concerning the principles and the objectives of the monetary authorities
(Calomiris et al., 2016; Nyborg, 2016; Bindseil and Laeven, 2017). The present analysis
extends, therefore, previous studies, which attempted to provide a quantitative setting
to inform such a debate (Ashcraft et al., 2011; Bindseil et al., 2017b; Bindseil and
Lanari, 2022). We add in particular to the stream of models that design explicitly the
features of the CBCF coupled with a sensible representation of the regulated financial
systems and its main building blocks, i.e. (i) the assets variety in terms of scope of the
investments or liquidity, (ii) the heterogeneity of the banks operating in the markets
with diverse business models, and (iii) the different strategies to deal with financial

4 Generally, an throughout this paper, a haircut refers to a parameter h ∈ [0, 1] such that the value

v of an asset is discounted to v = (1 − h) v.

5 On this regard, recall that insufficient buffers relative to short-term liabilities have been pointed
to be a trigger of the GFC, and one of the primary causes of an (at least temporarily) excessive
reliance on Central Bank funding (BCBS, 2013).

6 "[T]here is a trade-off to be struck.

Increased maturity transformation delivers benefits to the
non-bank sectors of the economy and produces term structures of interest rates more favourable to
long-term investment. But the more significant the aggregate degree of maturity transformation,
the more the systemic risks and the greater the extent to which risks can only be offset by the
potential for Central Bank liquidity assistance." (Turner, 2009)

ECB Working Paper Series No 28145shocks and market distress.

Figure 1: Types and amounts of used collateral for the ECB credit operation from Q1 2012 to
Q2 2021. Authors’ calculations on publicly available aggregate data available at https://www.ecb.
europa.eu/paym/coll/charts/html/index.en.html.

1.2 Contributions of the paper

On the background of previous studies, the model adds to the literature a stress test
model targeted to analyse the role of the central banks’ collateral framework as it
emerged during the last decade. Building on Cont and Schaanning (2017a, 2019) and
Cont et al. (2020), we introduce a model where shocks to assets values induce endoge-
nous liquidity shortfalls to which banks respond using diverse financing sources: asset
sales, unsecured credit, repo credit or Central Bank credit. Such an extension defines
multiple interactions in the solvency-liquidity landscape, leading to the amplification
of the exogenous shocks prompted as the starting point of the stress test.

The integration and the enhancement of Cont and Schaanning (2017a) and Cont
et al. (2020) allow us to account for multiple sources of loss amplification (or damp-
ening) whose intertwined effects constitute the significant aspects of novelty of the
proposed model. In particular, our model extends the following features of previous
studies:

1. Multiple liquidity categorisation. The model relies on two intertwinings
(but not identical) extensive asset liquidity categorisation: the one defined by
the parameters of the collateral framework and the one implied by the market
depths, enriching the constant haircut approach (Cont et al., 2020) and con-
stant market depth approach (Greenwood et al., 2015). This joint framework
provides a flexible analytical context to test how individual bank positions or

ECB Working Paper Series No 28146systemic stress outcomes respond to modifications of the collateral framework’s
parameters.

2. Banks liquidity strategies. The inclusion of multiple funding sources to deal
with assets’ value shock and liquidity shortfalls opens the issue of the strategic
behaviours of financial institutions. First, it is shown how the complexity of
the strategic landscape makes unlikely any global maximisation approach by the
agents since an optimal, or preferred, liquidity stress strategy (LSS) (adapting
the definition of Bindseil et al., 2017b) does not exist or is ill-defined in a con-
text of multiple funding sources with endogenous costs determination. Second,
extending Coen et al. (2019), we encode the effects of regulatory ratios as signals
and practical requirements to prevent liquidity shortfall or access to different
funding sources.

3. Systemic effects due to common asset holdings.

Indirect contagion is
transmitted through an implicit network defined using common asset holdings
based on the bank’s exposure classification. This way, institutions recurring to
fire sales to gather liquidity might induce losses on other agents in the financial
markets through price-mediated impact and mark-to-market balance sheet losses.

4. Solvency-liquidity interaction channels. Within a coherent solvency-
liquidity interplay, liquidity shocks are endogenously generated by funding short-
falls linked to the deterioration of banks’ fundamentals. The approach does not
require the introduction of exogenous liquidity shocks, allowing instead to test
whether i) shocks to a single asset class induce heterogeneous liquidity stress
according to institution-specific balance sheet characteristics7; ii) the impact of
different starting shocks on single financial institutions from a systemic perspec-
tive.

We propose two separate applications of the models. The first one is operating
on a simulated financial system with banks and investors/depositors, where balance
sheet typical values are simulated on the line of the empirical analysis by Farnè and
Vouldis (2021). The simulation allows specifying four bank business models, operating
in a market with discrete asset categories diversified in market depths, Central Bank
haircuts and private repo haircuts. Next, we present an empirical application. Our
framework suits an empirical decomposition of the balance sheets of the Eurosystem
banks based on integrating multiple data sources. The balance sheets of banks are
recovered using the Financial Information Reporting (FINREP) framework, which in-
cludes information on balance sheets, income statements and equity, financial assets

7 This enriches the widely adopted framework of homogeneous cash inflows/outflows of ECB liquidity

stress tests.

ECB Working Paper Series No 28147and liabilities at the bank level8. Moreover, the information on balance sheets is in-
tegrated by expanding the granularity of the exposures to non-financial corporations
through AnaCredit. The scope of AnaCredit covers loans to companies harmonised
across member states. Given the balance sheet representation, the single asset cate-
gories are then associated with category-specific market depths computed from publicly
available information on transaction volumes and market volatilities (as in Cont and
Schaanning, 2017a; Coen et al., 2019), and the information on haircuts from the public
Eligible Assets Dataset available at the European Central Bank.

With the above applications, we first test the effect of a collateral framework ex-
pansion on the financial system’s exposure to bank-specific and systemic losses. Next,
we compare the outcomes of stress tests in two cases: one in which banks have access to
multiple channels and, in particular, to credit-upon-collateral to deal with liquidity and
asset values shock, and the other in which the only available strategy is to sell assets
at endogenously determined market prices. In this respect, for both applications, we
confirm the intuition on the risk-mitigating effects of the collateral frameworks. How-
ever, we highlight that i) while homogeneous expansions of the collateral framework
have always a significant impact on equity losses, the benefits do not increase linearly
with the magnitude of the widening, yet become stationary after a certain threshold
in haircut reduction; ii) in the empirical application to the European Banking system
we quantify the reduction of the systemic losses, finding that relative systemic losses
estimates in a stress test are reduced up to 17% in the most severe scenarios and on
average are of around 5% when the financial institutions can rely on the collateral
framework channel.

1.3 Relevant literature

Our contribution relates to three main branches of the literature. First, we refer to the
literature on stress testing and financial stability. We model in one framework several
properties of two classes of stress tests. We include the price-mediated effects of fire
sales through correlated exposures (see Shleifer and Vishny, 2011, for a review on fire
sales), studying the induced losses and eventually the impact on the systemic stress
as in (Cont and Schaanning, 2017a; Coen et al., 2019) and the mitigation effect of
the collateral framework. We also represent the multiple funding sources of financial
institutions and the possible liquidity shortfall induced by credit-sensitive investors as
in Cont et al. (2020), yet relaxing the hypothesis on the pecking order of the available
mitigating strategies and giving a more realistic picture of the collateral framework.

8 Entities reporting to FINREP in our dataset include investment companies, banks and bank-
ing groups in the European Union subject to the Capital Requirements Directive IV (CRD IV).
More on FINREP can be found here: https://www.bankingsupervision.europa.eu/banking/
statistics/html/index.en.html.

ECB Working Paper Series No 28148Moreover, we relate the banks’ actions to the regulatory requirements as in Coen et al.
(2019).

Second, we enrich and extend the theoretical works modelling the Central Bank
collateralised credit operations. Our model improves upon Bindseil et al. (2017b) and
Bindseil and Lanari (2022), introducing a realistic framework designed to relax the
continuous liquidity hypothesis and explore the dynamics of the liquidity crisis in a
setting with boundedly rational heterogeneous banks and depositors. This framework
allows us to factor in the effects of the regulatory constraints on banks’ asset liqui-
dation strategies and, hence, better represent their liability structure, exploring the
impact of the collateral framework calibration on a financial system populated by
banks operating under different business models. Other classical models relevant to
this paper are Rochet and Vives (2004) modelling fire sales and Central Bank collateral
in a stylised two-asset world and the general multiple funding equilibrium literature,
as reviewed in Morris and Shin (2006). Relatively recent literature integrates Central
Bank credit into macroeconomic models (Gertler and Kiyotaki, 2015; De Fiore et al.,
2018). These contributions link bank runs to the Central Bank’s monetary policies in
a general equilibrium framework9 with continuous liquidity and ad hoc assumptions on
the limits to maturity transformation for the banking system (Ashcraft et al., 2011).
In that context, haircuts affect the leverage ratio, eventually influencing the costs of
assets and the shadow cost of equity: the financing costs are endogenously derived.
At the same time, banks and other agents are not heterogeneous. The inclusion of the
collateralised credit within a set of available macroprudential policies has also been
studied in some agents based models (ABMs), see, e.g. the rich framework outlined
by Popoyan et al. (2020) whereby, however, the collateral accepted in Central Bank’s
credit operations is limited to central government bonds.

Lastly, we contribute to the existing empirical works that focus on the banks’
strategic recourse to Central Bank credit triggered by exceptional policy measures
during a crisis and regular times (Berger et al., 2017; Cassola and Koulischer, 2019;
Drechsler et al., 2021). We offer, in particular, a theoretical perspective in designing a
framework whereby the effects of the haircuts broadening or tightening can be tested
in a policy scenario analysis. The model allows drawing some preliminary conclusions
on the bank lending channel of monetary policy Jiménez et al. (2012, 2014) and the
effects of unconventional monetary policies when the interest rate approaches negative
territories (Rodnyansky and Darmouni, 2017; Altavilla et al., 2021; Heider et al., 2019).

9 The authors model asset liquidity as a continuum yet adopting an analogous artefact to represent
the banks and impose heterogeneity gauging on the distributional properties of banks parametric
features, rather than sketching heterogeneity in terms of strategies and business models.

ECB Working Paper Series No 281491.4 Outline

The rest of the paper is organised as follows. Section 2 presents an operational
model for stress-testing a financial system where banks have access to multiple funding
sources, including the Central Bank collateral framework. Section 3 analyses the prop-
erties of the framework and discusses the banks’ allocation strategies in the liquidity
market. In Section 4 we describe the data used for the Euro Area banks, and Section
5 presents our empirical results. Section 6 concludes the article with a final remark.

2 Multi-faceted liquidity in a stress test model

We consider an operational model with NB financial institutions (or banks)10. The
proposed balance sheet representation distinguishes between marketable and non-
marketable assets, encumbered and unencumbered assets. The section outlines the
technical characteristics of the model in the following order:
i. the banks’ balance
sheet composition, ii. the definition of the shocks, iii. banks’ liquidity strategies, and
iv. the timeline of the model.

2.1 Banks’ balance sheet

i,µ = AM,enc

i,µ + AM,une

Let us consider KM marketable asset classes and KN non-marketable asset classes. We
for encumbered
denote the set of asset holdings of bank i as AM
i,µ
i,ν + AN,une
and unencumbered marketable assets (µ = 1, . . . , KM ), and AN
for encumbered and unencumbered non-marketable assets (ν = 1, . . . , KN ). Each of
these asset categories is endowed with two sets of asset characteristics. The first set
parametrises the conditions under which a unit of an asset can be transformed into
cash holdings and includes the market depths Dµ, the haircuts in the repo market
11. The second set includes risk weights
, hN,cb
hrp
ν
µ
) and liquidity coverage ratio (LCR) haircuts, defining the characteristic of
(ρM
µ , ρN
ν
the assets as determined by the regulatory environment12.

and the Central Bank haircuts hM,cb

i,ν = AN,enc

i,ν

µ

The liabilities of each bank are distinguished into six categories: equity, unse-
cured debt, Central Bank debt, repo debt, other long-term debt and deposits. The
total amount of deposits is calibrated, and their granular distribution is simulated by

10 In the following, we will equivalently refer to banks and financial institutions. The model adapts to
the possible inclusion of heterogeneous market agents regarding balance sheet composition, strategic
behaviour and interaction with the regulatory environment.

11 It will be evident in the following how these parameters enter the dynamics of the model. Market
depths are supposed to measure the liquidity of the market segment associated with that specific
market class and hence are related to marketable assets only. The same restriction applies to
collateral that is mobilised on the repo market. Relying on related empirical studies, we assume
that only marketable assets are used for repos (Schaffner et al., 2019; Julliard et al., 2019).

12 While risk weights are defined for both marketable and non-marketable assets, only high-quality

assets enter the computation of the LCR, hence hlcr refers to those assets only.

ECB Working Paper Series No 281410Assets side

Liabilities side

AM,enc
µ,i
AN,enc
ν,i

, AM,une
µ,i
, AN,une
ν,i

ci

oi

Marketable

ei Equity

Non-marketable

Cash

Other assets

lu
i
lrp
i
lcb
i
lot
i
ld
ik

Unsecured credit

Repo credit

Central Bank credit

Other credit

Short-term deposits

Table 1: Balance sheet representation for bank i.

defining a population of depositors/investors. The framework allows, therefore, for a
stochastic mechanism that models the differential credit sensitivity of diverse classes
of fundings, e.g. retail, wholesale, institutional and deposits with agreed maturity.
In addition, modelling short-term funding as an ensemble of heterogeneous depositors
has the following benefits. On one side, it is possible to capture the redistribution dy-
namics of wealth within the financial system if the depositors can withdraw deposits
and reallocate them to other banks. On the other hand, the wealth eroded because of
illiquid or insolvent banks provide a valuable indicator to measure the impact of the
financial shocks on depositors’ wealth at a systemic level.

2.2 Assets and liquidity shocks

As in Cont and Schaanning (2017a, 2019); Coen et al. (2019), shocks to assets’ values
are prompted as a starting event of the stress test. Any impact on asset prices is
transferred to banks’ balance sheets, inducing mark-to-market losses. Formally, a
vector of assets value shock is defined by

(cid:0)ϵM , ϵN (cid:1) = (cid:0)ϵM

1 , . . . , ϵM
KM

, ϵM

1 , . . . , ϵN
KN

(cid:1) .

(1)

where exogenous shocks take the most general form, with ϵM
taking any value
µ
between zero and one. On the contrary, shocks implied by some endogenous shift
in the market price apply only to marketable assets, meaning that ϵN
is necessarily
ν
set to zero. Assets value shocks, independently of their value or source, affect banks’
fundamentals: the immediate losses are absorbed via equity

and ϵN
ν

ei = ei −

KM(cid:88)

µ

µ AM
ϵM

µ,k −

KN(cid:88)

ν

ν AN
ϵN
ν,k

(2)

ECB Working Paper Series No 281411and transfer to the leverage ratio, the capital ratio (or risk-weighted capital ratio,
RWCR) and the liquidity coverage ratio (LCR)13

LR

i =

RWCR

i =

LCR

i =

ci + oi + (cid:80)KM

ν

µ

ei − (cid:80)KM

µ,i − (cid:80)KN

µ
(1 − ϵM

µ AM
ϵM
µ )AM
ei − (cid:80)KM
µ AM
ϵM
µ
µ,i + (cid:80)KN
µ )AM
µ (1 − ϵM
ρM
(cid:80)KM
µ
µ ωout · li − (cid:80)KM
µ ωin

ν AN
ϵN
ν,i
µ,i + (cid:80)KN
(1 − ϵN
ν AN
ϵN
ν,i
ν
ρnuN (1 − ϵN
)(1 − hLCR
µ )AM

ν
(1 − ϵM,une
µ
µ (1 − ϵM

µ,i − (cid:80)KN

ν

(cid:80)KM
µ

(cid:80)KM

ν )AN
ν,i
)AM
µ,i
µ,i + (cid:80)KN
ν ωN,in

µ

ν

ν )AN
ν,i

(3)

(1 − ϵN

ν )AN
ν,i

where li = (lu
ciated outflow weights ωout implied by the regulatory environment.

i , li,1, . . . , li,Di) is the vector collecting the liabilities with the asso-

i , lot

i , lcb

After a shock to the value of assets, the leverage ratio or the risk-weighted capi-
tal constraint may fall below acceptable levels and trigger the loss of credit-sensitive
funding. Such funding includes, for instance, retail deposits available for withdrawal
or short-term loans for which the rollover is no longer possible at acceptable market
conditions. In Cont et al. (2020) this is represented as a credit downgrade implied by
a fall in the leverage ratio. On the same line, we take as reference the RWCR and con-
dition the shortfall on the leverage ratio of the bank: credit-sensitive fundings run-off
if the RWCR falls below a threshold ξ and the probability of withdrawal depends on
the leverage ratio.

Even though we share the core idea, admitting that depositors’ runs are linked
to banks’ fundamentals and follow the downturn of business cycles (De Graeve and
Karas, 2014; Pereira et al., 2019)14, we nevertheless recognise that generally, investors
have different run-off rates and that their variability increases during financial distress.
In particular, the increased withdrawing rate also depends on coordinating the deposi-
tors’ behaviours, depending on heterogeneous liquidity needs and access to the relevant
information. Therefore, we model two classes of depositors that can be populated us-
ing the minimal information provided in standard balance sheets datasets: stable and
informed depositors. Stable depositors do not withdraw within the stress test horizon.
In contrast, informed depositors withdraw following the outcome of a stochastic vari-
able parametrised by the leverage ratio of the bank15. Then, the shortfall for bank i

13 Notice that we will refer in the following to the general notion of equity, while the capital ei refers
to Tier 1 capital in the case of the leverage ratio, while it refers to Common Equity Tier 1 in the
case of the risk-weighted capital ratio. Whenever the granularity of the balance sheet information
is sufficient, ei is replaced with the correct capital classification.

14 See Kiss (2018) for a review of the literature on the topic.
15 The framework is designed to allow for a more extensive heterogeneity of depositors. An example
is the category of ordinary depositors, stickier than informed depositors and following the lead of
other agents in the same bank when deciding. We have chosen to keep the depositor classification
minimal.

ECB Working Paper Series No 281412implied by depositors run at a given time step is:

i = E
λd

(cid:35)

ld
r,iXr,i

(cid:34)

(cid:88)

r∈Di

where Xr,i are independent Bernoulli random variables B(pr,i) where

pr,i =




0



e−δd LRi

if RWCRi > ξi
if RWCRi ≤ ξi

(4)

Analogously, other liabilities, such as repo and unsecured credit, shrink due to missed
rollover following

i = e−(δun LRi) · lun
λun

i

i = e−(δrp LRi) · lrp
λrp

i

and the overall liquidity shortfall for bank i is then equal to λi = λun

i + λrp

i + λd
i

(5)

.

2.3 Banks’ strategies

Banks can undertake several actions when cash holdings are insufficient to cover the
funding’s outflows or, more generally, if they are willing to modify their balance sheet
positions. The modelling options for these actions follow those implemented in Cont
et al. (2020) with two additional features.

First, we decompose the asset universe into discrete classes uniquely identified
by their market depth and private repo haircut, marketable assets, and Central Bank
haircut category for marketable and non-marketable assets. This representation marks
a significant difference between the extant contributions, which mainly rely on two
i) they rely on a one-dimensional representation of liquidity
modelling strategies:
focusing, e.g. on fire sales only as in Greenwood et al. (2015) (with uniform market
depths) or in (Cont and Schaanning, 2017a) and Coen et al. (2019); ii) they model
multiple liquidity channels but restrict the mobilisation of collateral to a single segment
of the liquidity spectrum, as in Cont et al. (2020) where the illiquid assets only are
used to back up the loans from the Central Bank or as in Popoyan et al. (2020) where
only government debts are pledged.

Second, we do not impose a strict pecking order of the operations since it is more
likely that banks operate by selecting their strategies according to i) the effective costs
of liquidity, depending on the market discounts for sales, or depending on the interest
rate and the applied haircut for the inter-bank and Central Bank credit operations16;

16 As explained in the introduction, we generally refer to haircuts as the difference between the
collateral value pledged in the bank’s balance sheet and the value of the loan issued by the Central
Bank. Our notion of haircut then includes any ex-ante valuation operation and any own-use or

ECB Working Paper Series No 281413ii) their needs and objectives, as the strategy changes if banks need to cover depositors’
withdrawals or balance their asset portfolio to restyle their regulatory ratios (Kedan
and Veghazy, 2021; Jasova et al., 2021).

Here, we list the equations defining the terms and conditions of each funding option

together with the implications for the capital and the regulatory indicators:17

1. Unsecured credit. Banks have access to unsecured credit at an exogenous interest
rate rU . When banks want to access this segment, the volume they obtain depends on
their fundamentals following the approach of Cont et al. (2020):

vU =

ei ψ − (cid:80)

µ,i − (cid:80)

µ AM
1 + rU ψ

ν AN
ν,i

(6)

where ψ is a parameter ruling the sensitivity to the banks leverage18, rU is the interest
rate for unsecured credit, and the costs of the operation are covered via equity:

ei − rU vU .

(7)

As for the rest, the impact on the regulatory ratios depends on the nature of the specific
operation. For example, if used to replace deposits, it might impact the LCR because
swapping deposits with unsecured credit changes the composition of the denominator.

2. Liquidity through repurchase agreements. To gather liquidity on the repo
market, a bank can mobilize unencumbered collateral in exchange for a volume vRP
that is modulated by the haircut applied to the value of the assets provided

vRP = (cid:80)

µ )AM,une

µ(1 − hRP
ei − vRP · rRP

µ,i

pRP
µ,i

(8)

(9)

where pRP is the amount of collateral mobilized in this channel and hRP
µ
specific private repo haircut.

the asset-

3. CB collateralized lending. As anticipated, banks can access Central Bank credit
if they hold and are ready to mobilise sufficient eligible collateral. The value of funding
raised depends again on the value of the assets pledged:

vCB = (cid:80)

µ(1 − hCB

µ )AM,une

µ,i

µ,i + (cid:80)
pCB
ei − vCB · rCB

ν(1 − hCB

ν

)AN,une
ν,i

pCB
ν,i

(10)

(11)

foreign currency add-on.

17 For the sake of the synthesis, we limit the explicit derivation to the equity and the leverage ratio,

the formulas for the remainder can be derived accordingly.

18 Note that since the volume of unsecured credit is constrained by the leverage the numerator of Eq.

(6) contains encumbered and unencumbered assets.

ECB Working Paper Series No 281414and pCB
ν,i

where pCB
are the relative amounts of marketable assets in the category µ
µ,i
and non-marketable assets in the category ν that are pledged, and rCB is the Central
Bank interest rate.

4. Assets sales. Banks can also opt to sell part of their disposable marketable assets.
The liquidity they gather varies with the fluctuations of the market prices determining
the market discounts. These eventually depend on the total volume of assets sold for
any specific category and the relative market depth. Following Donier et al. (2015),
Cont and Schaanning (2017a) and Coen et al. (2019), we define a linear price impact
function for the price of the asset µ:

∆µ =

(cid:80)

j sM

µ,i

µ,j AM,une
Dµ

(12)

is the relative quantity of assets in the category µ that bank j decides to
where sM
µ,j
sell. Once established that only marketable assets enter the dynamics of assets sales,
to keep the notation lighter.
we omit the suffix M for sM
µ,j

Price shifts induce a loss via two different channels. First, while liquidating sellers

accept the given market price and face an overall value reduction equal to:

Disµ,i = α

AM,une
µ,i
(cid:124)
(cid:123)(cid:122)
Sold unencumbered assets

sµ,i
(cid:125)

(cid:80)

j sµ,jAM,une
Dµ

µ,j

(13)

The coefficient α obtains the price impact as an average over the liquidation horizon.
Standard values are α = 1
and α = 1, the former assumes that assets are liquidated
2
with success uniformly over the liquidation horizon. At the same time, the latter re-
factors price impacts as if all the assets were sold at the final price. Second, all financial
institution needs to register balance sheets with mark-to-market losses mediated by
market price to their remaining holdings

Mtmµ,i =

(cid:16)

(cid:124)

(cid:17)

AM,enc

µ,i + AM,une

µ,i
(cid:123)(cid:122)
Remaining assets

(1 − sµ,i)
(cid:125)

(cid:32)

1 −

(cid:80)

j sµ,jAM,une
Dµ

µ,j

(cid:33)

(14)

In the actual implementation of the model, the first loss is registered coincidentally
to the sale process, while the second is prompted as an asset shock as in Eq. 1. The
overall collected cash is then

(cid:32)

S = αAM,une
vµ

µ,i

sµ,i

1 −

(cid:33)

(cid:80)

j sµ,jAM,une
Dµ

µ,j

ECB Working Paper Series No 281415and the impact on equity

ei = ei −

(cid:88)

µ

(1 − (1 − α)sµ,i)Aµ,i

(cid:80)

j sµ,jAM,une
Dµ

µ,j

(15)

2.4 Model’s timeline

With the given setup, we implement the following timeline:

i. A shock as per Eq. 1 hits the value of assets, and the banks register the induced
losses to the balance sheets. As a result, banks’ fundamentals (LR, LCR, RWCR)
change accordingly.

ii. Sensitive depositors or other lenders respond to the fundamental changes. At this
step, the shock may trigger a partial loss of funding due to deposits coordinated
withdrawal or missed rollover on the part of the repo or unsecured debt. This
defines the bank-specific liquidity shortfalls λi (i = 1, . . . , NB).

iii. All the banks in the financial system are called to action. Initially, they deal
with liquidity shortfalls or use the available funding source to restore the possi-
bly deteriorated fundamentals (LR, RWCR and LCR). Both the issues are faced
recurring to the funding sources described above. First, banks seek liquidity
through unsecured lending and then choose a strategy to mobilise or sell their
collateral, exploiting the various channels according to their objectives and col-
lateral availability.

iv. The undertaken mitigating actions affect the economic environment.

In par-
ticular, sales affect asset market prices. This change occurs because market
participants sell at the price they get from the market (see Eq. (13)).

v. Once the banks have implemented their strategies, the liquidity and solvency
of each financial institution are assessed: banks that are not able to cover the
liquidity shortfall default for illiquidity, banks that, after repaying, cannot face
the costs of the compensating borrowing and operate with negative equity default
for insolvency19.

vi. The mark-to-market losses mediated by asset prices (eq. (14)) are transferred to
banks’ balance sheet items in the form of assets value shock as in step 1. The
cycle closes and restarts.

With respect to the timeline and its graphical representations in Figure 2, we
provide three clarifying comments. First, a single round of timeline, from point (i) to

19 The inability to restore liquidity and capital indicators to acceptable levels is not a cause of

bankruptcy.

ECB Working Paper Series No 281416point (vi), is to be considered as a process at the weekly time scale. Thus, the model
horizon depends on the number of repetitions of the round that defines the timeline
and in our proposed applications, with 10 repetitions, it ranges between two to three
months. Second, with the model’s main equations, we outline an interaction between
balance sheet variables and the fundamental indicators derived from them. These
indicators are usually updated and published annually, and under current regulations
in the European Union, they become binding at this frequency. Nonetheless, they
can serve as indicators of the liquidity and solvency conditions of financial institutions
to informed and sensitive investors. For this reason, the updated indicators do not
directly affect the conditions of financial institutions, but rather, they interact with
the environment, either restricting or expanding the possibility of accessing unsecured
credit or triggering the withdrawal of credit-sensitive funding. Finally, we note that
the graphs in Figure 2 generalize the similar diagrams of Cont and Schaanning (2017a)
and Cont et al. (2020), with two relevant differences concerning the actions of banks. In
our framework, the position in the leverage diagram changes depending on the channel
used by the bank to restore its position and can result in multiple outcomes (see the
connections from C to D1, D2, D3). This broadens the potential for active balance
sheet changes in comparison to Cont and Schaanning (2017b) and Coen et al. (2019),
where the trajectories in the leverage diagram must always be linked to a reference
value for a complex dynamic. The position in the liquidity-solvency diagram, moreover,
evolves in a nonmonotonic manner due to the non-hierarchical and unordered access
to channels by banks, unlike the hierarchical and ordered access in Cont et al. (2020).

3 A simulated financial systems of heterogeneous

banks

We apply the model to a simulated financial system populated by heterogeneous banks
and depositors. The approach is common in previous stress test models (see e.g.
Cont and Schaanning, 2019; Cont et al., 2020) and it is intended to give a theoretical
overview of the model properties in a controlled environment.

3.1 Assets and liquidity categories

Table 2 summarises the parameters defining the liquidity landscape. Our simulated
classification distinguishes 12 asset categories based on the corresponding market depth
(first row in Table 2). Next, each class of market depth is split into three subclasses
defined by a unique combination of CB haircuts and repo haircuts20. A total of 36

20 The values are chosen to scale in line with (ECB, 2020) and to give enough variability to test the
model, while repo haircuts are in line with the data offered by the Acceptable Collateral haircuts

ECB Working Paper Series No 281417(a) Liquidity-solvency diagram.

(b) Leverage reference diagram.

Figure 2: Bank’s liquidity-solvency and leverage-reference diagram. On top of the evolution of the
timeline from the perspective of the capital and liquidity positions. Though represented as generic
indicators, one can measure capital using equity and liquidity using cash and highly liquid collateral
(or any other liquidity indicator). At the bottom, is the timeline from the perspective of the leverage
ratio. Certain exogenous events or bank actions do not affect the position directly (B=C) or might
affect it along diverse paths. For example, C-D1 is the typical path for asset sales aimed at restoring
the leverage above a threshold level, C-D3 is the typical path of collateralized credit, and C-D2 is the
result of a mixed mobilization.

liquidity classes gives an exact partition of the assets universe. Risk weights for the
computation of the RWCR and haircuts of the LCR are defined for the 12 initial

of the LCH Clearnet group.

ECB Working Paper Series No 281418A1
100

0.01
0.005
0.01
0.01
0.02
0.025

A2
50

0.03
0.01
0.02
0.02
0.04
0.06

A3
20

0.03
0.02
0.02
0.02
0.02
0.04

A4
13

0.03
0.025
0.04
0.04
0.04
0.05

s
t
u
c
r
i
a
H

CB
Repo
CB
Repo
CB
Repo

Risk weights
LCR hcs

0
0

0.1
0.1

0.1
0.15

0.2
0.15

Market depths (bn EUR)
A8
0.5

A7
0.9

A5
5

A6
1

A9 A10 A11 A12
0.3

0

0

0

0.04
0.03
0.08
0.08
0.06
0.08

1
0.03
0.04
0.04
0.06
0.08

0.05
0.03
0.05
0.04
0.1
1

0.1
0.08
0.08
0.08
1
1

1
0.08
0.1
0.1
0.15
1

0.2
0.1
0.15
1
0.2
1

0.25
1
0.2
1
0.1
1

0.4
1
0.35
1
0.3
1

Regulation parameters
1
0.35
0.8
0.2

0.5
0.2

0.7
0.8

1
1

1
1

1
1

1
1

Table 2: Asset categories identified by a unique combination of market depths, CB haircuts and
Repo haircuts. Null market depths are assigned to non-marketable assets, while when the haircuts
are equal to one, they are not accepted in that specific credit segment.

categories and are reported at the bottom of Table 2.

3.2 Model initialisation

The environment is populated by two macro groups of agents: NB = 50 banks and
ND = 50000 depositors21. Banks belong to one of the four business models inspired by
the clustered figures provided by Farnè and Vouldis (2021) for the Euro Area banking
system, in the context of the supervisory reporting of the SSM, defining four sub-
populations distinguished by the relative amount of the liabilities items. The general
characteristics of each subpopulation are reported in Table 3 for the categories that are
relevant to our application. The values set the reference points around which each sub-
population of banks distributes when the model is initialised22. Reference loan share
populates the three categories A10-A12 uniformly in the table above. In comparison,
the remaining percentage of assets is assigned to the 27 remaining categories following
the typical distribution of the liquidity overlaps as in Cont and Schaanning (2017a)23.
The size of banks is drawn from a lognormal distribution with mean and variance at
the bottom of Table 3.

Each depositor deposits at a maximum of 5 banks. The distribution of deposits is
Pareto-like so that the total amount of deposits matches the values for each bank24.
Depositors can be of two types defined above, stable and informed, with stable depos-
itors being 70% of the total depositors’ population and uniformly distributed across
banks.

21 The ratio between depositors and banks numbers is only illustrative. Anyway, as anticipated
above, one should think of the depositor representation as a way to parametrise the stochastic
process modelling the run-off of credit-sensitive fundings.

22 The distributions are Gaussians centred in the reference share with variance reported in parenthesis.
23 See Fig. 8 therein and notice that the construction of the matrix of liquidity weighted overlaps is

independent on the number of the assets categories.

24 Distributions parameters are designed to guarantee an approximated match of the depositor-bank
relation, minor corrections of banks and depositors sizes are implemented when the model is ini-
tialised to ensure consistency, but the distributions remain substantially unchanged.

ECB Working Paper Series No 281419CC

SH

TC

WF

Deposits
Debt
Equity

35% (3%)
50% (5%)
15% (1%)

40% (3%)
50% (5%)
10% (1%)

25% (3%)
60% (5%)
15% (1%)

30% (3%)
55% (5%)
15% (1%)

Loans share

55% (5%)

75% (5%)

75% (5%)

60% (5%)

N banks
Size parameters

18
23 (0.7)

21
21 (0.4)

12
23.5 (0.7)

29
22 (0.6)

Table 3: Mean and variances (in parenthesis) for the relative quantities for the key items in the
banks’ balance sheets for each subpopulation. Reference values are borrowed from the cluster analysis
of Farnè and Vouldis (2021). Number of banks for four different bank business models and parameters
of the lognormal size distribution for each subpopulation. CC = Complex Commercial; SH = Security
Holding, TC = Traditional Commercial, WF = Wholesale Funding

Parameter
NB
ND
ξi
δd
δun
δrp
ψ

Description (reference formula)
Total number of banks
Total number of depositors
RWCR limiting threshold (4)
Depositors run-off sensitivity (4)
Unsecured credit run-off sensitivity (5)
Repo run-off sensitivity (5)
Access to unsecured credit sensitivity (6)

Value
80
5 · 105
0.08 ∀i
15
+∞
+∞
15

Table 4: Parameters summary for the simulated scenario.

The remaining model’s parameters are summarized in Table 4. Notice that for this
first test of the framework, we restrict the sources of liquidity shocks to the run-off of
informed depositors while modelling sticky the other funding sources.

3.3 Properties of the model

We simulate the timeline of the model for 10 iterations and given that the model is not
fully deterministic due to the stochastic processes ruling the depositors’ and banks’
choices, we present the outcome as the average of 20 different runs.

Looking at banks’ defaults, we infer from the representation in Figure 2a that after
the initial shock, banks’ paths have two main possible trajectories in the liquidity-
solvency diagram: either they sell assets or they search for collateralized credit. The
path followed is determined by the initial shock but depends on the unfolding dynam-
ics of the environmental (systemic) variables after that. Systemic effects mark the
difference with stress test models restricting the analysis to a single bank’s balance
sheet (see e.g. Cont et al., 2020) and generate complex interactions within agents in
the financial system. Fig. 3 shows the number of defaults at each step for various
shock intensities prompted to non-marketable assets (A10-A12 of Table 2). For our
simulated system, we observe that insolvency is the most common mode of failure,
while only a few units are illiquid. Failures due to illiquidity anticipate and foster the
subsequent rounds of insolvency defaults induced by price-mediated contagion. Non-
contemporaneity is determined because price shocks transfer to balance sheets at the

ECB Working Paper Series No 281420end of each step and internalise at the beginning of the following step. In other words,
if the shock is strong enough to induce liquidity defaults in a few banks, the recourse
to fire sales of these banks and other shocked institutions triggers a price spiral that
eventually affects bank solvency.

As in Cont and Schaanning (2017a), the mere fact that both failure modes are
possible is not a distinctive feature of all stress tests. Duarte and Eisenbach (2021)
and Greenwood et al. (2015) model all assets as readily available for deleveraging
so that they can never be illiquid in practice. In general, deleveraging models only
model illiquidity as the impossibility to restore their leverage ratio above a subjective
threshold (including of Cont and Schaanning, 2017a), and not as a funding run-off
that banks cannot counterbalance. Fig. 3 also shows the existence of a minimal level
for a shock to have system effects and trigger a series of insolvency failures. For the
analysed system, that is around a 4% shock to all the classes of non-marketable assets
(columns A10-A12) in the configuration of Table 2. The existence of thresholds is
confirmed by the output of Fig. 4 which shows a clear jump in the equity loss per
banking type between 4% and 5%.

Regarding the evolution of bank fundamentals, our extension differs from models
where the value of a single indicator is used as a reference for the mitigating actions
In such models, the multiplicity
(Cont and Schaanning, 2017a; Coen et al., 2019).
of linkages between the dynamics of financial distress and the fundamental indicators
of the banks is limited.
In our setting, therefore, the solvency-liquidity interplay
determined by the susceptibility of credit-sensitive fundings and the inclusion of the
collateral framework among the mitigating actions originate a complex evolution of
banks’ regulatory ratios.

Notice that the intensive and extensive margin determines a shift in the regulatory
ratio distributions. Namely, they can also change because the active (non-defaulted
banks) population shrinks. Fig. 5 shows the evolution of the LCR and the RWCR
distribution for the four bank types. We notice how the crisis unfolds at different
paces according to banks’ balance sheet composition. Focusing on a bank from group
4, we see that banks in that class have the instruments to sustain their capital ratio
throughout the evolution of the crisis, drawing from their reserves of high-quality
assets or cash and thus depleting their liquidity coverage ratio. However, the opposite
dynamics are also possible. Banks in group 3, for example, have almost constant
median LCR. At the same time, the RWCR, which had already deteriorated after the
initial shocks, declined significantly and fell below the levels defined by the regulatory
minima.

ECB Working Paper Series No 281421(a) Illiquid banks.

(b) Insolvent banks.

Figure 3: The number of defaults for different time steps and intensity of the initial shock.

(c) Total number of defaults.

3.4 Stress outcomes and the collateral framework

As an experimental setup, we analyse the sensitivity of the results to the Central Bank
haircut values by modelling the policy’s responses to the Covid-19 crisis that occurred
between March and April 2020 in the Euro Area. At that time, the Governing Council
of the ECB “decided to temporarily increase its risk tolerance level in credit operations
through a general reduction of collateral valuation haircuts by a fixed factor of 20%” 25.
We prompt, therefore, a 5% shock and 6% in non-marketable assets values, to which
the Central Bank responds by reducing the haircuts, modulating the intensity of the
easing from -5% to -25%. We analyse stress tests of the ten-time steps each, and the
outcomes presented are again the simple average of 20 runs.

25 https://www.ecb.europa.eu/press/pr/date/2020/html/ecb.pr200407~2472a8ccda.en.html.

ECB Working Paper Series No 281422Figure 4: Bank equity losses for different business models and different initial shocks. Note: CC
= Complex Commercial; SH = Security Holding, TC = Traditional Commercial, WF = Wholesale
Funding.

Figure 5: Distribution of the liquidity coverage ratio (LCR) and risk-weighted capital ratio (RWCR)
per bank business model. The sequence shows the evolution in the first seven steps after an initial
shock of the 5% for non-marketable assets. Note: CC = Complex Commercial; SH = Security Holding,
TC = Traditional Commercial, WF = Wholesale Funding.

0.0020.0040.00264Initial shock (%)Second−round loss (as % of total equity)Bank type: CCSHTCWF5% shock to non−marketables − Banks fundamentals Bank type:  CC  SH  TC  WFLCRRWCR123456750.00100.00150.00200.000.005.0010.0015.0020.0025.00Time steps(%)ECB Working Paper Series No 281423Looking at defaults (Fig. 6), we notice that there is a threshold after which the
expansion of the collateral framework affects financial stability. The threshold varies
with the shock level and tends to reduce around 15% of the haircuts in our proposed
setting. Secondly, we observe that the broadening of the collateral framework almost
exclusively affects the insolvency defaults. As anticipated in section B, such a finding
can be explained by the fact that the collateral framework broadening not only changes
the condition under which banks access liquidity at the Central Bank but also limits the
banks’ recourse to other funding channels eventually dampening the market turmoil.
Fig. 7, 8 and 9 show the differential effect of collateral broadening on equity loss
and other fundamentals. Looking at the capital loss, the impact of a change to the
collateral framework seems homogeneous across different bank types, with banks in
group 2 benefiting more from the intervention than the other types.

Figure 6: Illiquid and insolvent banks for 5% and 6% shocks to non-marketable assets for different
values of collateral framework expansion

4 Data for the Euro Area

The model as it is designed is particularly demanding in terms of the granularity of
the data sources. Recent developments in bank-level data reporting and harmonisation
allow recovering an empirical decomposition of the balance sheets of the Eurosystem
banks based on the integration of the Financial Information Reporting (FINREP)
and the Analytical Credit Datasets (AnaCredit) of the European System of Central
Banks. Such a decomposition of the balance sheets can be integrated with the key
characteristics of the collateral framework and information on asset liquidity.

Illiquid banksInsolvent  banks5.06.05.06.00.003.006.009.00Initial shock (%)Number of defaultsIntervention intensity: −25%−20%−15%−10%−5%ECB Working Paper Series No 281424Figure 7: Bank equity losses after ten steps given an initial shock of 5% to non-marketable assets for
different bank types and under the different interventions of the Central Bank. Note: CC = Complex
Commercial; SH = Security Holding, TC = Traditional Commercial, WF = Wholesale Funding.

Figure 8: Bank-specific equity losses after ten simulation steps vs the initial loss after the exogenous
shock (as a percentage of bank equity). Results for two levels of intervention. Note: CC = Complex
Commercial; SH = Security Holding, TC = Traditional Commercial, WF = Wholesale Funding.

We apply the model to 67 significant institutions in the Euro Area.26 The section

briefly describes the data and defines our structure of asset classes.

26 Significant institutions are identified by criteria of size and economic relevance. For a description of
the criteria, see https://www.bankingsupervision.europa.eu/banking/list/criteria/html/
index.en.html.

0.0010.0020.0030.0040.00−25%−20%−15%−10%−5%Initervention intensitySecond−round loss (as % of total equity)Equity loss − 5% shock to non−marketables Bank type: CCSHTCWFIntervention: −15%Intervention: −5%5.07.510.012.55.07.510.012.510.0020.0030.0040.0050.0060.00Loss after initial shock (as % of total equity)Final loss (as % of total equity)Bank−specific equity loss − 5% shock to non−marketables Bank type:    CC       SH       TC    WFECB Working Paper Series No 281425Figure 9: Distributions of the liquidity coverage ratio (LCR) and risk-weighted capital ratio (RWCR)
per bank type. Snapshot of the values at the tenth simulation step of the stress test under different
Central Bank intervention intensities compared with the initial distributions (left side). Note: CC
= Complex Commercial; SH = Security Holding, TC = Traditional Commercial, WF = Wholesale
Funding.

4.1 Granular representation of banks’ balance sheet

We build the banks’ balance sheets using the Financial Reporting Framework (FIN-
REP) and AnaCredit, the instrument-level dataset of the ECB, as of December 2021.
We divide assets into tradable and non-tradable assets 27. Both asset types are then
additionally distinguished between encumbered and unencumbered assets.28 While all
assets are differentiated by country, loans to non-financial corporations are then disag-
gregated across the following dimensions: i) country, ii) type of counterpart, iii) type
of securitisation, iv) industrial sector (NACE 2), v) class of risk, and vi) maturity.29

A novelty of the paper is the joint use of Finrep and AnaCredit as data sources.
In addition to Finrep, AnaCredit enriches balance sheet data with information on

27 See Tables C.2 and C.3.
28 see Tables C.4 and C.5 and Appendix D.
29 We consider countries in Euro Area and include Denmark, Norway, Sweden, Great Britain, Switzer-
land, Australia, New Zealand, USA, Canada, China, Hong Kong, Japan, South Korea, and Singa-
pore (the main OECD economies). All other countries are aggregated in a single foreign economy.
See Table C.6 for the composition of balance sheets across the country of counterpart and Table
C.7 for the detail of the country composition for non-financial loans based on AnaCredit. Types
of counterparts include central banks, government, non-financial institutions, and other financial
institutions. The type of securitisation distinguishes between traditional securitisation, synthetic
securitisation, and not securitised. We construct three risk classes using the probability of default
reported in AnaCredit, i.e.
lower than 0.1, between 0.1 and 0.4, and above 0.4 (see Table C.8).
The probability of default is reported at the loan level. If the loan level value is missing, we then
consider the average probability of default in the industrial sector. Classes of maturity distinguish
assets into three classes: below 3 years, between 3 and 7 years, and above 7 years (see Table C.9.

LCRRWCRInit−25%15%−10%−5%0.0050.00100.00150.00200.000.005.0010.0015.0020.0025.00−20%                     − Intervention intensity(%)5% shock to non−marketables − Shocked banks fundamentals (final step)Bank type:  CC  SH  TC  WFECB Working Paper Series No 281426the encumbrance, the type of securitisation, the industrial sector, the risk, and the
maturity of each bank instrument. Since the scope of the two datasets can differ30,
we disaggregate the aggregate value of non-financial institutions’ assets reported in
Finrep by the relative weights computed using AnaCredit. Such an approach ensures
that the aggregate sum of assets remains unchanged, while it allows disaggregating
assets by type of securitisation, industrial sector, class of risk, and classes of maturity.
We are, therefore, able to include more than 500 asset classes.

4.2 Asset liquidity

As for the simulated model, the asset classes are characterised by a triple of parameters:
market depth, Central Bank haircut and repo haircut. This approach shares the
perspective of heterogeneous liquidity models as Cont and Schaanning (2017a) and
Coen et al. (2019), in contrast to Greenwood et al. (2015) which assume a uniform
market depth of 109 (EUR bn).

For the market depths, we apply a linear impact model for the marketable asset µ:

Dµ = c

ADVµ
σµ

√

τ

where ADV is the average daily trading volume (in EUR), σµ the daily volatility (in
% points) associated with the asset class and τ is the liquidation horizon, and c is a
coefficient set equal to 0.3 as in Cont and Schaanning (2017a)31. As for the parameters,
τ is set to be equal to 10 for a liquidation horizon of two weeks and c = 0.3 as in Cont
and Schaanning (2017a). On the chosen impact function, just notice that while finer
liquidity measures are available and can be more reliable and precise, this one allows
us to get estimates from publicly available data and to get a consistent integration
with the balance sheets decomposition outlined above.

Volatilities are obtained from the daily S&P returns for the specific asset categories
and countries32,33,34. We get the estimates of the ADV for government bonds from
public authorities, governments and central banks online sources (see Coen et al., 2019,
for a detailed list of references for both volatilities and volumes). Data on daily volumes
for corporate bonds and equity instruments are available only for the US at SIFMA35,

30 AnaCredit contains records only for consolidated positions above 25.000 euros and only for legal

entities (e.g. households are not included)

31 The coefficients generate from square root model for market depth, and its derivation is beyond
the scope of this paper. We refer to Cont and Schaanning (2017a) for a thorough discussion on the
adequacy of this price impact measure and its calibration.

32 Government bond indices https://www.spglobal.com/spdji/en/index-family/fixed-income/

treasury-sovereign-quasi-government/sovereign/#overview.

33 Equity indices: https://www.spglobal.com/spdji/en/index-family/equity/.
34 Corporate bonds indices: https://www.spglobal.com/spdji/en/index-family/fixed-income/

corporates/#indices.

35 https://www.sifma.org/resources/archive/research/statistics/.

ECB Working Paper Series No 281427we integrate the figures for the other countries using BIS outstanding amounts36 and
assuming proportionality of the turnover ratio. For example, taking government and
equity volumes and exceptional amounts for the US, a parameter κ is estimated as37:

ADVU S
e
OAU S
e

= κ

ADVU S

g
OAU S
g

and then for a generic country (C):

ADVC

e = κ

ADVC
g
OAC
g

OAC
e

When data are not available at the mentioned references, we set the associated market
depth as null and assume that the particular exposure is non-marketable.

Central Bank haircut estimates for the asset categories are obtained from the El-
igible Assets dataset (Sept 2021)38. Simple averages are taken for each unique asset
type, debtor group and country. For non-marketable assets, the categorization im-
posed through the AnaCredit variables allows settling the haircuts in agreement with
the ECB official guidelines ECB (2020).

For repo haircuts, we get a proxy for the primary government instruments from

the accepted collateral haircuts of LCH Clearnet.39

4.3 Stress scenarios

We define stress scenarios as exogenous shocks to selected asset classes given the above
representation. A vector of percentage loss defines shocks (see Eq. (1)) and is imparted
to the balance sheets at the beginning of the timeline defined in section 2.4. We define
three scenarios:

1. EBA 2021: we use the losses implied by the 2021 EU-wide stress test of the Eu-
ropean Banking Authority as a benchmark. That exercise provides information
on the envisaged losses under two scenarios for 50 European banks within three
years (2021-2023). We calibrate a diffused shock to non-marketable assets to
match exactly the bank-specific shift in the leverage ratio under the adverse sce-
nario40. In practical terms we take as input ∆LRi for bank i from EBA (2021b)
and set

36 https://stats.bis.org/statx/srs/table/c1.
37 In complete analogy, the turnover ratio is also used for corporate bonds and other instruments.
38 https://www.ecb.europa.eu/paym/coll/assets/html/list-MID.en.html
39 See

https://www.lch.com/collateral-management/ltd-collateral-management/

ltd-acceptable-collateral/ltd-acceptable-securities

40 For all the relevant information on the definition of the two scenarios, the bank included and the

general methodology see EBA (2021a).

ECB Working Paper Series No 2814281 = . . . = ϵM
ϵM
KM

∆(LRi) = 1 −

= 0
LRi
i(α)

LR

1 = · · · = ϵN
ϵM
KN

= αi

s.t.

(16)

LR

i(α) =

ci + oi + (cid:80)KM

ν AN
ν,i

ei − α (cid:80)KN
µ AM

µ,i + (1 − α) (cid:80)KN

ν AN
ν,i

The bank-specific leverage ratio loss is specified for 33 banks that are the in-
tersection between the EBA dataset and ours. The institutions not included in
the EBA datasets are shocked using the country means or the overall mean if
the country is absent. Notice that it is an asymmetric shock, and its calibration
through the EBA exercise is fundamental to understanding the differential im-
pact on European banks. However, when implementing the test, we regulate the
intensity of the shock, rescaling uniformly the coefficients αi. The scaling factors
define five intensity profiles. I1: 0.05, I2: 0.1, I3: 0.15, I4: 0.2, I5: 0.25.

2. Russian shock: Losses materialize with different intensities on sovereign expo-
sures and commercial and retail exposures of Russia and nearby countries with
five different intensities profiles according to Table 5.

Country

Assets

RU
RU
RU
EE, LT, LV, SK SI
EE, LT, LV, SK SI Loans to non-financial corporations

Government and regional debt
Loans to non-financial corporations
Loans to households
Government and regional debt

I1
0.5
0.5
0.5
0.01
0.01

Assets value shock
I3
0.75
0.75
0.75
0.1
0.1

I4
0.8
0.8
0.8
0.15
0.15

I2
0.6
0.6
0.6
0.05
0.05

I5
0.8
0.8
0.8
0.2
0.2

Table 5: Shocked assets and intensity profile for the Russian scenario.

3. Southern European shock: Losses materialize with different intensities to
non-financial corporations and households of southern European with five differ-
ent intensities profiles according to Table 6.

Country

Assets

IT, PT, ES, CY, GR, MT Loans to non-financial corporations
IT, PT, ES, CY, GR, MT

Loans to households

I1
0.01
0.01

Assets value shock
I3
0.1
0.1

I4
0.15
0.15

I2
0.05
0.05

I5
0.2
0.2

Table 6: Shocked assets and intensity profile for Southern European countries scenario.

5 Results

The severity of each scenario depends on different balance sheets composition and, in
particular, on the exposure in the regions and segments subject to the initial shock.
Table 7, provides the average initial loss (in % of equity) for selected intensities. We

ECB Working Paper Series No 281429Scenario
EBA

Scenario
East. cnt

Scenario
South. res.

Average equity loss (%)

Init. loss
Tot. loss

I1
1.27
8.99

I3
3.30
11.04

I5
5.32
13.59

I1
1.11
8.43

I3
1.58
9.38

I5
2.09
9.78

I1
1.58
9.64

I3
14.32
24.10

I5
25.47
34.21

Table 7: Average percentage losses of the stress scenarios. The initial losses are those induced by
the exogenous shock, while total losses materialize at the end of the stress test.

notice that even minimal initial shocks at the initial step are sufficient to trigger sub-
stantial losses in the aggregate at the end of the ten steps. For the applied shock
intensities, we do not find evidence of the existence of a tipping point in the shock
intensity line as in Cont and Schaanning (2017a). The endogenous dynamics unfolding
after the initial shock determine a smoother transition from a status of financial sta-
bility to the materialization of the systemic losses implied by the indirect contagion.
This appears from the surface plots for the Eastern country scenario (Fig. 10b) and
the Southern residential scenario (10c).

(a) Defaults for EBA scenario.

(b) Defaults for Eastern European scenario.

(c) Defaults for Southern scenario.

Figure 10: Number of defaults for different time steps and intensity of the initial shock

ECB Working Paper Series No 281430Fig. 10a reports the results for the EBA scenario. While it is characterized by
asymmetric the intensity of the shocks, in the sense that they affect different banks
with different intensities, the EBA scenario is homogeneous to the asset classes as the
initial value shock is deployed to all non-marketable assets of all banks, irrespectively
of their exposures towards particular markets or segments. In this light, we can in-
terpret the constant level failures, independent from the shock value and occur after
a few iterations, as defaults induced directly by the initial shock on banks that enter
the stress test with already deteriorated fundamentals. This evidence suggests that
the experiment should be extended to higher levels of intensity shocks to generate
significant aggregate dynamics.

To strengthen our results, we provide a quantitative analysis of the collateral frame-
work’s role in supporting the European financial system during periods of stress. The
analysis compares the relevant indicators where banks can use assets as collateral in
lending transactions versus cases where they raise liquidity only by selling them. Re-
sults indicate that, on average, stress testing with the collateral framework leads to
the preservation of 5% equity losses across all three scenarios and all the intensity
profiles, with system losses increasing from 18.19% to 23.06% (Fig. 11). The effect is
also evident when considering the lower end of the distribution. It is more pronounced
as the intensity and severity of the scenario increase, with equity losses in the ’Only
Sales’ model exceeding the collateral framework model by 16 points. Fig. 11 shows
differences between the scenarios as the intensity profiles change, with the effect of the
collateral framework being constant in the case of shocks to assets linked to Eastern
countries and increasing as the intensity rises for the other two scenarios, particularly
for the southern country residential scenario. This suggests that for shocks involving
more banks and a broader class of assets, as those of EBA and southern residential
scenarios, the collateral framework induces a reduction in asset sales, thus supporting
prices and slowing down the contagion mechanism at each round. This explains why
the gains in terms of equity losses increase more than linearly.

Fig. 12 shows the evolution of the distributions of fundamentals for the entire
financial system. The two versions of the model for the three scenarios are compared
under the intensity profile I3. The results show that the collateral framework supports
banks’ fundamentals, particularly at the first step after the exogenous shock. Over
time, the median values for the two models get closer, primarily due to the differ-
ential impact of the selection effect. With 5-10% more defaults mainly occurring in
the second part of the time span, in the ’Only Sales’ specification, most banks with
deteriorated fundamentals are selected out and do not participate in the aggregate
statistics. Two other points are worth noting. First, the collateral framework con-
tributes significantly to supporting all fundamentals, with a significant difference for
the three distributional quantiles considered, albeit with some differences. Second,

ECB Working Paper Series No 281431Model
With CF
Only Sales

Min Loss (%) Average Loss (%) Q90 Loss (%) Q99 Loss (%) Max Loss (%)

6.70
8.99

18.19
23.06

39.00
48.48

63.55
79.67

66.52
83.85

Figure 11: Comparison between a simulation with the collateral framework and asset sales only.
System-wide average bank equity loss as a percentage of initial bank equity for different scenarios
and intensity profiles. Entries in the table display the minimum, maximum and average total losses
in percentage points across different scenarios and intensity profiles.

the model provides evidence that banks with strong fundamentals (those in the 90th
percentile) interact strategically with the collateral framework. As a consequence, an
increase in the value of the 90th percentile of the main fundamentals in the first steps
after the shock is to be interpreted as an overreaction of the banks willing to improve
their condition, restoring the level of the indicators above a subjective threshold well
above the regulatory requirements. This is what happens, for example, for the capital
ratio (RWCR) in the EBA and southern residential scenarios.

Making the most use of our granular dimensions, we show that shocks affect coun-
tries asymmetrically (Fig. 13) and asymmetric is the impact of a collateral framework
modulation or removal (Fig. 14)41. Previous observations on the EBA scenario are
confirmed by looking at the distributions of the regulatory ratios (Fig. 13a). The
dynamics for most countries are restricted to the initial shock and the immediate af-
termath, showing evidence of a general spreading of the variances of the distributions,
which stabilize from the third step onward. We observe interesting dynamics for a
small country with few banks (last on the right). The subsequent shocks to assets
value and loss of funding continue to bite, causing a general depletion of asset values

41 The scope of Fig. 13 and Fig. 14 in the present working paper is to highlight the differential
evolution and effects for different jurisdictions and not to illustrate country-specific stress levels.
Hence the panels refer to non-overlapping pools of anonymized countries. Country-specific results
are going to be developed more in detail in future works.

ECB Working Paper Series No 281432Figure 12: Time evolution of the distribution of the banks’ fundamentals (median, 10th, and 90th
percentile) comparing simulations with the collateral framework and asset sales only. Intensity profile
= I3 (Tables 5-6)

transferred directly to the leverage ratio. The same holds for the Russian shock sce-
nario (Fig. 13b) where the distributional shifts after the first step are almost entirely
restricted to the leverage ratios distribution of a single country.

For what concerns the Southern European shock scenario (Fig. 13c), the inten-
sity of the initial shock generates sustained endogenous dynamics that are probably
restricted to countries that are most exposed to the domestic residential market. In
particular, for a country (the last on the right), the initial shock causes significant
losses transferred directly to the capital and leverage ratio. The subsequent recov-
ery is explained by failing banks leaving the population of active institutions, while
second-round adjustments are due to the interaction with the liquidity environment.

Finally, Fig. 14 zooms into country-specific distributions of the fundamentals,
where the selection effect has been controlled for including in the analysed sample only
the banks surviving until the end of the stress test. This outcome helps highlight how,
while the general mitigating impact is confirmed, the effects of the collateral framework
can be heterogeneous across jurisdictions depending on the scenario considered, with
some cases showing zero or reversed signs. These differences being more and more
significant as we disaggregate to the bank level.

6 Concluding remarks

This paper develops a stress test model for a system of heterogeneous banks where
multi-faceted liquidity shapes the outcomes of stress test outcomes. The proposed
setting relies on a granular representation of banks’ balance sheets which need to

ECB Working Paper Series No 281433(a) EBA scenario (I5).

(b) Eastern countries scenario (I5).

(c) Southern residential scenario (I5).

Figure 13: Distributions of the liquidity coverage ratio (LCR), the leverage ratio (LR) and the
risk-weighted capital ratio (RWCR) for five selected countries (anonymized). Evolution at different
simulation steps

LCRLRRWCR1234567891020.0954.60148.412.725.447.397.3920.0954.60Time steps(%)LCRLRRWCR1234567891020.0954.60148.412.725.447.397.3920.0954.60Time steps(%)LCRLRRWCR1234567891020.0954.60148.410.371.002.727.391.007.3954.60Time steps(%)ECB Working Paper Series No 281434Figure 14: Distributions of banks fundamentals for five selected countries (anonymized). The
columns display i) the distributions after the initial shock, ii) the end-of-simulation distributions for
the model with the collateral framework (CF), and iii) the Only-Sales model (OS). Country averages
are reported beneath the box plots. For all the columns, the sample is restricted to banks non-
defaulting until the end of the simulation

ECB Working Paper Series No 281435distinguish asset classes along three liquidity dimensions defined by the characteristics
and the terms of the exchange between the asset and readily available cash. The
marketable assets can be sold at a market price that depends on a given market depth
or used as collateral in a transaction in the private repo market or with the Central
Bank at the conditions established in the Central Bank collateral framework. This
framework outlines an operational framework where liquidity and solvency positions of
banks non-linear interact in the unfolding of a financial crisis generated by exogenous
shocks. The asset price movements determine systemic effects and thus depend on
the intertwining of the network of common exposures and the haircuts and eligibility
requirements for collateral. The stress test model relies on a granular representation
of the balance sheet and allows to condition and measure of the banks’ performances
using regulatory ratios as representations of banks’ fundamentals.

The model finds that systemic losses are reduced up to 17% in the most severe
scenarios and on average around 5% when the collateral framework channel is available
to banks. We emphasise, therefore, the importance of the Central Bank collateral
framework as an instrument for financial stability.

We show how modelling a granular collateral framework significantly modifies the
strategy space of banks facing a liquidity shortfall and eventually transforms the liq-
uidity landscape by mitigating the turmoil in asset prices. Testing the model on a
simulated financial system highlights the relevance of heterogeneity in the assessment
of the impact of the collateral framework. If models were overlooking the heterogeneity
of the balance sheet composition and banks’ liquidity positions, they would undermine
two relevant policy targets, i.e. asset market stability and fostering credit supply. On
the former aspect, especially, we show how heterogeneous banks have likely divergent
liquidity stress strategies and, consequently, their impact on asset market prices in
a crisis might vary consistently. The effectiveness of central bank policies would be,
therefore, enhanced by factoring in the asymmetric effects of haircuts when calibrating
the collateral framework parameters to stabilise asset markets.

As for the outlook, with a theoretical simulation of the model, we highlight how
the model’s main properties can be used to address policy-relevant conclusions in
future applications. The model can be used, for instance, to confirm the Bagehot
“inertia principle”: i.e. avoiding an expansion of the collateral framework, even though
it might seem to prevent excessive reliance on Central Bank resources in the short
run, could eventually lead to the opposite result. A milder reaction could in principle
destabilise a larger share of banks that suffer from impaired access to market funding.
Recourse to Central Bank credit, therefore, would be wider and prolonged to phase
the financial system out of a crisis.

In the paper, we show how in stress test models where banks under stress could face
a crisis via various mitigating actions, banks’ strategies are relevant in the definition of

ECB Working Paper Series No 281436the outcomes. To better capture the systemic effects of banks’ activity, therefore, an
empirical analysis of the patterns of collateral mobilization in the private repo market
(Schaffner et al., 2019) or to the Central Bank (on the line of Jasova et al., 2021) is a
natural complement for the model.

Nonetheless, the current study is constrained by some of its assumptions, which
leave room for future extensions. To begin, we simulate constant haircuts for assets and
the repo market, whereas haircuts may change during a crisis. Similarly, we use a linear
function for asset pricing here, whereas non-linear functions could be tested to better
fit price reactions during times of distress. Following that, an expanded modelling
of depositor expectations could broaden the bank-run mechanism: we present here a
trigger mechanism that can be fine-tuned using alternative behavioural mechanisms.
Finally, we do model online indirect bank contagion via common exposures, so the
paper does not examine direct contagion coming from possible second-round effects
due to bank defaults. We leave potential extensions to future research.

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ECB Working Paper Series No 281444Appendix A. The collateral framework as a policy tool: a his-

torical overview

Collateral frameworks of central banks (and their predecessors) have been frequently
used for policy purposes, i.e. have been specified not only to serve risk protection
but also to reach specific further public policy objectives. We will list in this section
ten examples across the history of central banks and finally assign those in six classes
according to the pursued policy goals, whereby sometimes measures supported more
than one such goal:

i) Monetary policy: if collateral policies aim to achieve a monetary policy objective,
such as price stability. The collateral framework can become decisive for mone-
tary policy if conventional monetary policy is constrained by zero lower bounds.
In this case, collateral policies can support banks in maintaining bank interme-
diation spreads moderate and therefore contribute to low refinancing costs of the
economy for a given level of policy rates.

ii) Ex-ante liquidity policy: if the collateral framework aims at supporting the liq-
uidity of financial markets and the ability of intermediaries to deliver liquidity
transformation, such as to also moderate term and liquidity spreads and make
favourable financing conditions for longer-term investments.

iii) Restoring ex-post financial stability: if the collateral framework aims at restoring

financial stability after the outbreak of a liquidity crisis.

iv) Structural/industrial policy: if collateral policies aim at supporting real growth,

either in general or via a specific industry, that is considered crucial.

v) Addressing market failures: if collateral policies aim at correcting an identified

market failure that, e.g. distorts relative financial market prices.

vi) Social policy:
households.

if collateral policies aim at supporting low or very low-income

The model proposed in this paper does not cover all the objectives and rather focuses
on financial stability. We nevertheless mention in this section all the policy goals to
provide a comprehensive picture of the role of the collateral frameworks of central
banks.

The initial motivation of any collateral requirement is to protect the lending Cen-
tral Bank from financial losses in case of a default of the borrower. Therefore, this
perspective is also the first basis for establishing which assets are eligible, valuing
It is universal because any commercial
collateral carefully, and imposing haircuts.

ECB Working Paper Series No 281445entity without policy objectives will determine its collateral framework based on such
considerations.

Consider now the ten examples throughout history.

(1) A public lending facility to save the poor from usury: the Italian Monti
di Pietà as of 1463 and the Hamburger Bank in 1619. Monti di Pietà were
one early predecessor of central banks. Their lending facilities were integrated via
the Naples public banking system (starting in the 1580s), the Hamburger Bank (1619)
and the Stockholm Banco (1658)/Riksens Ständers Banco (1668) into central banking.
However, their initial motivation was social: to prevent poor citizens from taking
recourse to private “usurers” who would eventually harm the debtors more than help
them (Muzzarelli, 1999; Barile, 2012; Carboni, 2012). The Hamburger Bank took up
this social aspiration of the Monti di Pietà in 1619, of which the preamble of the
statutes of its lending-arm states (Bindseil, 2019, p. 25):

According to experience, which also has been reported bitterly to the City
Council, people who need to borrow substantial amounts of money in an
emergency or for their business have to pay excessive interest rates and
pledge collateral, to egoistic, advantage-seeking individuals, in contradic-
tion with Christian love. Therefore, the City Council, to help the deserving
poor and anyone else, has decided to establish a lending bank (Lehn Banco)
with the following specification, such that everyone can as of now get fund-
ing there at a fair interest rate

The Hamburger Bank was the first Central Bank that both issued means of payments
and provided at the same time Lombard loans to citizens and firms. Of course, this
function would be contained if haircuts would be very high, or if the valuation of
collateral submitted would be very low. Therefore, both were soon identified as im-
portant parameters. Article 23 of the Statute of the Monte di Pietà di Siena of 1472
specifies that the pledge needs to be worth “at least a third more than the amount
that is lent”, which implies a haircut of 25%. The Monte di Pietà in Bologna in 1514
(article 6 of the statutes) foresees already a differentiated haircut schedule (whereby
the differentiation seems to be risk-based):

And such a Custodian shall be bound to value the pledges faithfully and
fairly. And if the pledges are of gold or silver, he shall lend according to
the valuation of two parts of the pledge, and no more; but if they are robes
or other things, he shall lend only half the valuation of such pledges.

The Statutes of the Monte di Pietà of Rome (1581, article 18) set collateral eligibility
requirements by excluding only certain specific items:

ECB Working Paper Series No 281446He shall lend money with regards to any type of stuff, except for offensive
or defensive weapons, furs, grouped yarn, giving advice on gold and silver
coated items that may be faulty and especially that the pledge will suffice

(2) Lending facilities of Monte di Pietà to support the financial liquidity of
the economy (last decades of 15th century). The economic ex-ante effects of the
lender of last resort function (LOLR) of Monte di Pietà is described in a surprisingly
modern way by Cerreti (1752, 12-13), referring to the effects of the creation of the first
Monte in Perugia in 1463:

The public soon felt all its usefulness [...]. The trader who pressed to pay
a bill of exchange would have perished for not daring to borrow a sum on
his goods, for fear of undermining his credit, found in the Mont de Pitié a
secret and assured resource that would make his fortune. For such a trader
has gone bankrupt for several million, owing it only to the scandalous usury
of a first loan of four or five thousand pounds. Individuals who previously
bought only with reserve, fearing, if something went wrong, that they would
be forced to borrow at high interest on their goods, or to sell them at a
considerable loss, bought, thanks to the Mont de Pitiè, with more boldness
and confidence, by the certainty of finding, if need be, money on the items
purchased. Beyond a useful circulation of commerce[...]. This beneficent
morning dew also spread over creditors and debtors, who both had the
satisfaction, one of extinguishing his debt, the other of receiving his claim.

In other words, the existence of a public LOLR generally strengthens funding liquid-
ity in a way that supports economic development. For example, the ECB justified
collateral measures similarly over the last 10 years (see below).

(3) The Hamburger Bank as Lender of last resort in 1763. The Hamburger
Bank acted as full-scale LOLR in 1763 and was probably the first comprehensive
such Central Bank use of collateral policies to restore financial stability after the
outbreak of a crisis (Bindseil 2020, Section 5.2, p. 144). In 1763 a major financial
crisis swept through the entire northern European financial centres (originating mainly
from Amsterdam; see e.g. Schnabel and Hyun Song, 2004). Many banking houses and
merchants were on the brink of default. On 3 August, the Hamburger Bank announced
that it would be ready to provide an exceptional amount of Lombard credit to bank
houses of up to one million Mark Banco with a maximum duration of 6 months (indeed
an exceptional amount compared to the usual end of year balances of Lombard loans).
The 1 million Mark Banco were exhausted on 9 August, and the merchant banking
houses then requested unlimited Lombard credit against precious metals. Moreover,

ECB Working Paper Series No 281447the question arose of how to extend credit beyond the usual counterparties, i.e.
in
particular to ordinary merchants who were now subject to acute liquidity stress as
financing through bills of exchange had broken down. (Soetbeer, 1886), also quoting
text from 1763, reports that:

Under these circumstances, the Senate of the City passed on 26 August
the following message to the chamber of commerce ‘He [the Senate] has
directed, after the current economic developments and their sad conse-
quences for the merchants and the public credit had begun, its thoughts
towards the question, if no means and ways could be identified, to support,
through collateralised lending against merchandise or other assets, some
honest merchant, who is in principle solid, but because of the unexpected
fall of other foreign and domestic merchants, is under stress to make timely
payments according to his commitments’. To this was associated an invi-
tation to submit one or the other feasible plan, if one could find such, and
implement it. While recognising ‘that it is difficult, to find a mean with
the intended effects, which is not associated with many inconveniences’ the
plan of a Lombard facility managed by the Admiralty was submitted three
days later.

The belief that debtors who are “solid but temporarily illiquid” are candidates for
benefitting from the LOLR thus dates back to at least 1763. The Admiralty scheme
consisted, according to Sieveking (1933) in the Bank lending to the Admiralty as
of 8 September 1763 500,000 Mark Banco; the Admiralty itself acted as (principal)
intermediary and lent the money to merchants against collateral (that the Bank would
not have accepted). The Admiralty of Hamburg was the highest port authority, which
was run by merchants and members of the City Council. A particularly broad collateral
set was accepted. To access the Admiralty Lombard facility, the merchants had to get
their goods taxed by sworn brokers and could borrow upon them up to two-thirds of
the estimated value, at the moderate interest rate of 0.25 per cent per month. Twenty
merchants took initially recourse to credit for a value of 287,000 Mark Banco, providing
as collateral: oil, tobacco, sugar, coffee, etc. This credit provision was in addition to
the standard Lombard facility of the Hamburger Bank, which itself reached high levels.
Today, most economists associate Bagehot’s Lombard Street of 1873 as being at the
very origin of central banks’ lender of last resort experience and awareness. However,
it is interesting to note that for Bagehot the Bank of England was not unique, since
he was explicitly referring to “other similar banks” (p. 87):

[The Bank of England] must in time of panic do what all other similar
banks must do; that in time of panic it must advance freely and vigorously
to the public out of the reserve [...]. The end is to stay the panic; and the

ECB Working Paper Series No 281448advances should, if possible, stay the panic.
[...] these advances should
be made on all good banking securities, and as largely as the public ask
for them. The reason is plain. The object is to stay alarm, and nothing
therefore should be done to cause alarm. But the way to cause alarm is
to refuse someone who has good security to offer. The news of this will
spread in an instant through all the money market at a moment of terror;
no one can say exactly who carries it, but in half an hour it will be carried
on all sides, and [P. 88] will intensify the terror everywhere [...]. The great
majority, the majority to be protected, are the ’sound’ people, the people
who have good security to offer. If it is known that the Bank of England is
freely advancing on what in ordinary times is reckoned a good security—on
what is then commonly pledged and easily convertible—the alarm of the
solvent merchants and bankers will be stayed. But if securities, really good
and usually convertible, are refused by the Bank, the alarm will not abate,
the other loans made will fail in obtaining their end, and the panic will
become worse and worse.

In short, central banks must at least preserve collateral availability in financial crisis
situations if they want to contribute to overcoming the crisis. They must not restrict
their collateral framework, and they must not even let paper lose their eligibility in a
crisis because e.g. liquidity or credit quality temporarily deteriorates.

(4) French railway companies in the 1850s. Already Kindleberger (1984) high-
lights the role of accepting railroad bonds as collateral by the Banque de France during
the economic upswing in the 1850s (“The boom of the 1850s, for example, was by no
means solely the result of the [gold] discoveries of 1849 and 1851.
[...] The Credit
Mobilier, first established in France in 1852, and later the action of the Banque de
France in admitting railroad securities to discount in 1856, were of greater importance
than the discoveries [...]”)

According to (Leclercq, 1982), “After the coup which led to the ‘Second Empire’, the
government asked the Banque de France to accept the railway companies’ bonds and
equities as collateral in discount operations and also for loans to any private person. It
also asked the Banque de France to lend money to the railway companies ahead of new
issuances and to place such issuances in the market. These measures helped the railway
companies in financing their activities, at a time when they have faced constraints and
had been prompted to merge among themselves by the government”. These measures
gave significant support to the development of railway companies in France at the
time until these companies, weakened in particular by rather high debts, were later
forced into mergers and nationalised. The measures included not only favourable
treatment of the railway companies’ bonds and stocks in the Banque de France’s

ECB Working Paper Series No 281449collateral framework, but also purchases of these bonds and stocks by the Banque de
France. While the purchases likely played a significant role, the same applied to the
collateral framework measures, as shown by the fact that the amounts of credit granted
by the Banque de France and the amount of railway company bonds and stocks used as
collateral increased significantly in the years following the abovementioned decisions,
as reported in (Plessis, 1985, pp. 113-114). Further analysis related to the Banque de
France’s historical collateral framework can be found in Bignon and Jobst (2017).

(5) The German “Lombardverbot” for Russian Government bonds in 1887.
In the 1880s, the “Lombardverbot”, the ineligibility of Russian bonds as collateral in
Reichsbank Lombard loans (Kindleberger, 1984, p. 227) would lead to major capital
flows between Russia, France and Germany and would be one step amongst many
towards WWI.“In the German Foreign Office about this time, Herbert Bismarck, the
Chancellor’s son, proposed forbidding bank advances on Russian securities as an act
of economic warfare [. . . ] on 10 November 1887, an order was issued forbidding banks
to lend on Russian securities – the famous Lombardverbot. Prices of Russian bonds
fell further in Germany; some were bought back by Russian investors, a great many
by French.” The Lombardverbot was eventually lifted only on 26 October 1894. It
however had a lasting impact on foreign debt allocation within Europe and contributed
to making French investors the by far largest group of victims of the ultimate Russian
default arising with the Red revolution.

(6) Lowering haircuts by Reichsbank in 1925 to support long term agricul-
tural credit. Hjalmar Schacht mentions in his book about the stabilisation of the
mark (Schacht, 1927) a number of measures undertaken by the Reichsbank in 1925
to support long term credit to agricultural enterprises. One of these measures was
that “the Reichsbank accepted a considerable additional number of covered bonds as
collateral for Lombard loans of the Reichsbank and increased the maximum loanable
amount from 50% to 75% (i.e. lowered haircuts from 50% to 25%). The result was a
surprising upwards movement of covered bond valuations, which supported the inflow
of substantial additional new funds also from other investors to agriculture” (see also
the Annual Report of the Reichsbank for 1925, page 9).

(7) Collateral measures to address the financial crisis in 2008. Before and
even more after the default of Lehman, the large majority of central banks around the
globe softened and broadened their collateral frameworks. In the words of the BIS
Markets Committee (Committee et al., 2013, pp. 8-9):

During the height of the financial crisis in 2008–09, a number of central
banks introduced, to varying degrees, crisis management measures such

ECB Working Paper Series No 281450as a temporary acceptance of additional types of collateral, a temporary
lowering of the minimum rating requirements of existing eligible collateral
or a temporary relaxation of haircut standards.

For example, the ECB announced such measures in a press release dated 15 October
2008. The Executive Board Member in charge of Market Operations at that time
justified the measures in a speech of 10 November 2009 as follows (González-Páramo,
2009):

Accordingly, the set of measures implemented by the Eurosystem – our
enhanced credit support programme – were designed with the objective of
providing support to the banking sector by: (a) helping the functioning of
the money market, (b) easing funding conditions for banks, and (c) im-
proving market liquidity in segments of the private debt securities market
(specifically, the market for covered bonds) that represent an important
source of funding for euro area banks. Through these measures, the ECB
aimed to mitigate the risk of systemic illiquidity in the euro area bank-
ing sector and to guarantee a steady flow of banking credit to euro area
households and firms.

These measures are both ex post measures, to address the tightening resulting from
the crisis and to prevent defaults, as well as forward looking ex ante measures which
want to encourage banks to provide fresh credit which would not be the intention of a
pure emergency measure aiming at preventing acute bank defaults.

(8) ECB collateral measures to address sovereign debt crisis in Europe
(2009-2015). Collateral availability can tighten without active measures by the Cen-
tral Bank, for example if a deterioration of credit quality of important debt issuers
leads to them losing eligible issuer status, or if they become subject to higher haircuts.
This was an important challenge not only in the Lehman crisis, but also in the subse-
quent euro area Government debt crisis. While the ECB had lowered the general rating
threshold in October 2008 from A- to BBB-, a number of countries subsequently fell
below that lowered threshold, namely Greece, Portugal, and Cyprus. We focus below
on the case if Greece. The measure was announced on 3 May 2010:

The Governing Council of the European Central Bank (ECB) has de-
cided to suspend the application of the minimum credit rating threshold
in the collateral eligibility requirements for the purposes of the Eurosys-
tem’s credit operations in the case of marketable debt instruments issued or
guaranteed by the Greek government. This suspension will be maintained
until further notice. The Greek government has approved an economic and

ECB Working Paper Series No 281451financial adjustment programme, which has been negotiated with the Euro-
pean Commission, in liaison with the ECB, and the International Monetary
Fund. The Governing Council has assessed the programme and considers
it to be appropriate. This positive assessment and the strong commitment
of the Greek government to fully implement the programme are the basis,
also from a risk management perspective, for the suspension announced
herewith

Unfortunately, the Greek program eventually fell off-track and the ECB felt obliged
on 4 February 2015 to suspend the waiver “as it [was] currently not possible to assume
a successful conclusion of the programme review”. The ECB re-instated the waiver
for Greece on 22 June 2016, when it could again “acknowledge the commitment of the
Greek government to implementing current ESM programme and expects continued
compliance with its conditionality”. In the meantime, Greece went through a period of
bank holidays and capital controls which became necessary as the Greek government
did not comply with EU/IMF program conditionality and fuelled discussions on an exit
of Greece from the Euro area. Financing conditions were of course highly unfavourable
for Greek firms during this episode.

(9) ECB collateral measures to address the COVID crisis – monetary policy
at the zero-lower bound. Facing the COVID-2019 crisis, a number of central banks
relaxed their collateral framework, despite the fact that credit quality of issuers and
counterparties did not improve. As an example, the unprecedented package announced
on 7 April 2020 by ECB includes a general reduction of the credit operations haircuts
(from ECB Press release):

The Governing Council of the European Central Bank (ECB) today
adopted a package of temporary collateral easing measures to facilitate
the availability of eligible collateral for Eurosystem counterparties to par-
ticipate in liquidity providing operations[...]. The Eurosystem is increasing
its risk tolerance to support the provision of credit via its refinancing op-
erations, particularly by lowering collateral valuation haircuts for all assets
the Governing Council decided to temporarily increase
consistently[...].
its risk tolerance level in credit operations through a general reduction of
collateral valuation haircuts by a fixed factor of 20%.

Indeed, the Covid crisis and the associated market volatility created exceptional col-
lateral (margining) requirements by CCPs, which put banks under stress, and which
made the ability to rely on the Central Bank for sourcing liquidity particularly impor-
tant (see e.g. ISDA, 2021). Moreover, the ECB had reached the effective lower bound
to its interest rate setting already from 2014 to 2019, when the still valid rate of the

ECB Working Paper Series No 281452Figure A.1: A schema classifying the ten examples across history of central banks in
six classes according to the pursued policy goals.

deposit facility of -0.5% was reached. In such a context, as the model of Bindseil and
Lanari (2022), the lowering of haircuts can have similar effects on monetary conditions
as a lowering of interest rate have.

(10) ECB collateral measures to address climate change. Last but not least,
central banks (ECB, 2021), NGOs (Dafermos et al., 2021) and academics (Shoenmaker,
2019) have identified the collateral framework as important instrument in supporting
the transition to a more climate friendly economy. In July 2021, the ECB launched
an action plan to include climate related considerations into the definition and imple-
mentation of its monetary policy

Within the mandate of the ECB, the climate change agenda will affect
the collateral framework in two fundamental aspects. First, disclosure re-
quirements for private sector assets will be introduced as a new eligibility
criterion or as a basis for a differentiated treatment for collateralized credit.
Second, haircuts modelling and calibration will reflect all relevant risks, in-
cluding those related to climate change. Third, the ECB committed to
support actively innovation in the area of sustainable finance, accepting
sustainability-linked bonds as collateral.

ECB Working Paper Series No 281453Appendix B. Deleveraging and liquidity-stress management

with multiple funding sources and discrete assets

classes

In this section we discuss the role of banks behaviours in a financial market with
discrete asset classes. These classes feature different liquidity levels along several
dimensions, any of this dimensions being identified by the potential use case for each
unit of asset. Since in the presented framework assets can be mobilized within different
channels and serve diverse bank’s objectives, the adopted modelling alternatives for
banks’ allocation choices may affect the outcome of the stress test.

That the assumptions on how agents choose to mobilize assets have a significant
impact on stress testing outcomes has already been noticed by Coen et al. (2019) in a
model of deleveraging through fire sales only. In that context, two main perspectives
span the sets of modelling assumptions. The first assumes that banks deleverage their
assets following simple heuristics, usually selling proportionally across asset classes
(Greenwood et al., 2015; Cont and Schaanning, 2017a; Duarte and Eisenbach, 2021).
In practical terms, if a bank with holdings of 10% in bonds, 30% in ABSs and 60% in
loans needs to sell 10 units on the market, she will try to sell 1 unit of bonds, 3 of ABSs
and 6 of loans. The second assumption states that financial institutions determine a
pecking order of the asset classes (Braouezec and Wagalath, 2018, 2019; Coen et al.,
2019; Bindseil and Lanari, 2022), usually maximizing the expected liquidation value
or other performance indicator associated to the allocation vector.

Comparing the two perspectives in a pure-sales framework, Coen et al. (2019) show
that a system where banks adopt proportional selling might suffer systemic losses five
times larger then a system where banks optimize over the possible liquidation strate-
gies, this happens because agents sell large amounts of illiquid assets even when they
could gather the needed liquidity relying on their high quality instruments. However,
the optimization approach to the banks’ allocation problem seems to be viable only in
simple models where the options and the objectives are limited and controlled. In a
system where banks can sell or pledge their assets, for example, the model of Bindseil
and Lanari (2022) derive optimization results only when liquidity is a one dimensional
property on a continuous interval. When that hypothesis is relaxed, with four liquid-
ity classes and assuming that assets in each class are pledged or collateralized in full,
Bindseil et al. (2017b) show that any dominant strategy does not emerge within the
strategy space.

For what concern our operational model, we endorse the perspective of agents based
models (ABMs) and represent banks as agents that follow agents-specific behavioural
rules. Among the possible behaviours, the modellers can opt for analytical or com-
putational optimization — if and when the optimization problem is well defined and

ECB Working Paper Series No 281454admit solutions — or rather heuristics that represent realistic behavioural patterns.
Moreover, we show here how the general setting outlined in the previous section defines
a liquidity environment whose state configuration is characterized by a high degree of
complexity and Knightian uncertainty, for two reasons mainly. First, some of the key
parameters for the strategies’ evaluation are known to the agents only after their de-
cision is taken. This happens because banks are price taker and decide to sell part of
their assets facing a discount on the initial price that depends on the strategy of the
other financial institutions, through the total amount sold. Second, the actions of the
banks have an effect on an intertemporal dimension: encumbering assets through any
of the available channels might be the best solution at a certain time step, but the
encumbered collateral might worth more for the bank if mobilized later as the liquidity
landscape changes.

Here we provide an overview of the banks liquidity-stress management in the frame-
work outlined by our operational model. Thus, we consider the general allocation prob-
lem for the portfolio of assets of a single bank accessing to three funding sources (assets
sales, Central Bank collateralized credit and the repo market), facing possible liquidity
shortfall and targeting a set of three capital and liquidity requirements. Notice that
not all the constraints are uniformly binding in any scenario. Onn one side, some of
the requirements might be overlooked by the bank during the (short-term) horizon of a
financial crisis, e.g. when the regulation is relaxed at the crisis outbreak, while on the
other side, banks might aim at over-compliance for certain regulatory requirements.
This is the case of financial institutions targeting a capital ratio (RWCR) or a LCR
well above the required threshold (see e.g. Grandia et al., 2019, for the LCR). In our
framework, this means that the banks might want to acess the various funding sources
to restore their fundamentals even when they comply with the regulatory requirements
and do not face any liquidity shortfall42.

Formally, consider a bank facing a total liquidity shortfall of λi ≥ 0 and with
leverage ratio LRi, liquidity coverage ratio LCRi and risk weighted capital RWCRi. In
a market environment as that defined in Section 2. We define an allocation strategy
as the set of vectors:

xi = (si, pRP

i

, pCB
i

) = (si, pRP

i

, pCB
i

)

where each vector collect the share of unencumbered assets allocated to the sales,
the repo market and the Central Bank credit operations. The dimensionality of the
i) non
problem in considerably high, but it reduces after few simple considerations:

42 A thorough analysis of this issue is out of the scope of this work. Notice however that the proposed
framework is flexible enough to model the bank’s strategic recourse to the Central Bank’s credit
with the aim to restyle their regulatory requirements. Empirical evidence on their behaviours and
their effect on monetary policy implementation has been collected recently in Grandia et al. (2019)
and Kedan and Veghazy (2021) among the others.

ECB Working Paper Series No 281455marketable assets are not available to be sold and are not accepted as collateral in the
repo operations and ii) the overall sum of shares needs to stay below one. This means
),
that after a further breakdown of the vectors si = (sM
i
the set of possible solutions restricts to

i = (pRP,M

i ), pRP

, pRP,N
i

, sN

i

Si = (cid:8)xi | sN

ν,i, pN

ν,i = 0, sM

µ,i + pM

µ,i + pM

µ,i ≤ 1 , pN

ν,i ≤ 1(cid:9)

As anticipated, covering possible liquidity shortfall might not be the unique purpose
of a financial institution. In general, she might be willing to drive all or some of their
.
liquidity and capital indicator values above certain threshold43: φLR
, φRW CR
i
Thus the general problem consists of selecting one point in the space defined by the
set of equations44:

, φLCR
i

i

vS(xi) + vCB(xi) + vRP (xi) ≥ λi

e(xi) ≥ 0
LR(xi) ≥ φLR

i

, LCR(xi) ≥ φLCR

i

, RWCR(xi) ≥ φRW CR

i

(B.1)

where the first line is the sum of the liquidity collected along the three channels, while
the other two encode the constraints on equity and on the regulatory ratios. The
system (B.1) defines the set of viable allocations as the set of points Vi ⊂ Si, satisfying
(B.1).

At this stage one can impose the agents to search for an optimal strategy in the
sense that it maximizes the ex post equity (e(xi)), while fulfilling the other constraints.
This is possible in the current setting only after neglecting the endogeneity associated
with fire sales discounts45. Here we focus rather on the analysis of the space of the
viable strategies to show how optimality may be ill defined in a context of market
interactions.

One of the strengths of our framework is that the dynamics of the stress scenario
unfold even when agents do not perceive the regulatory requirements as binding and,
i)
in general, it allows to model a wide heterogeneity of behaviours, for example:
banks overlooking regulatory requirements when dealing with liquidity shortfalls and
adjusting the values for the ratios only when not in liquidity need; ii) banks operating
in the liquidity market for restyling the ratio event when their are above the threshold.
In the remainder of this section we show how any maximization problem defined on

43 As noted above, the reference values for the threshold might be imposed by the regulatory author-

ities or rather being subjectively determined by the agents.

44 Note again here that we define the updated quantities using the underlined notation and that

throughout this section we explicit their dependence from the strategy vector xi.

(cid:80)

j AM,une

45 Indeed, Coen et al. (2019) replace the vector of total sales q in (13) (whose elements are qµ =
sM
µ,j), with the vector of sales of the the bank i. An other option consists of modelling
a complete strategic game and has been applied to a context of fire sales only in Braouezec and
Wagalath (2019).

µ,j

ECB Working Paper Series No 281456the space of viable strategies Vi is ill-defined in a context of discrete asset classes
and multiple funding sources for three main reasons. We conclude providing a brief
presentation of the algorithm that we implemented for the applications of the model
in the next section46.

A rugged strategy space. The first is that even choosing a single performance
indicator for a strategy xi, analytical maximization is not an option and computational
maximization is unfeasible in Vi, because any process of grid search scales with the
dimension of the space (the number of assets categories) and other search algorithm
are likely to get stuck in a local maximum since the viable-strategy space is rugged.
Consider the equity implied by a chosen strategy ei(xi) as a first measure of the
performance and calculate its value for one hundred thousand points (of Vi). After
choosing a reference point and a suitable metrics the viable-strategies space can be
rendered in a 3D surface plot as shown in Fig. B.1. With a simple visual inspection of

Figure B.1: The rugged implied equity landscape of the viable-strategies subspace for a generic
bank. On the x-y plane points represent the Canberra distance of each strategy component from a
fixed reference strategy. On the z-axis the implied equity relative to the initial equity is reported.

the plot it can be noticed that the space seems to have the basic characteristics of a
rugged landscape (Levinthal and Warglien, 1999) and it is confirmed when we consider
some basic topological measure. Look for example at the density of the locally optimal
strategies. To get a proxy one can look at the share of strategies reducing the equity of
one percent 1% within the strategy reducing the equity of the 5%, therein the density

46 As already mentioned the model can be adapted to any form of strategy definition or search,
including proportional deleveraging. Moreover different agents can implement different exploration
behaviours.

ECB Working Paper Series No 281457of the strategies is just the 0.85% (on average across the tested banks)47. On the same
line, the histogram in the top left-corner of Fig. B.2 shows exactly how strategies are
increasingly rare as we restrict to those that minimize equity loss.

Multiple performance indicators. The second reason against a maximizing ap-
proach is that agents might pursue multiple objectives while seeking liquidity. They
might want to reduce equity losses but also preserve liquid assets to cover potential
future losses in the development of the crisis. Fig. B.2 gives a first insight on this issue.
While some performance indicators display high level of correlations, as the case of
RWCR loss and equity loss, other might have low or absent correlation, meaning that
it would be unfeasible to maximize along a direction while preserving the rest. For
example the same bank willing to minimize her equity will try to sell or pledge the
most liquid assets (in terms of market depths). Indeed, assets with high market depths
are likely to get lower discounts and imply lower equity losses. However this naturally
leads to a decline in the liquidity potential of the portfolio of disposable assets of the
bank.

Figure B.2: Performance of the tested strategies along four dimensions defined by four selected
performance indicators: equity loss, RWCR loss, LR loss and HQ used assets. Comparison for a
sample of ten thousands tested strategies for 80 banks facing a fixed liquidity shortfall of 5% of total
assets.

47 For this experiment we tested all the banks inizialized according to the simulated model described

in the section below imposing a fixed liquidity shortfall of the 5% of total assets.

Eq. loss0.0050.0200.010.020.030.040.052.00e+092.10e+090.0050.0150.0250.91***RWCR loss0.51***0.68***LR loss−0.040.000.022.00e+092.10e+090.010.030.050.26***0.38***−0.040.000.28***Used assetsECB Working Paper Series No 281458Figure B.3: RWCR shift compared with three different assets destination for diverse funding sources
Comparison for a sample of ten thousands tested strategies for 80 banks facing a fixed liquidity
shortfall of 5% of total assets.

Strategies in a changing environment and an endogenously determined liq-
uidity landscape. The third reason we discuss concerns the impossibility to set up
a maximization problem when the parameters defining the problem change within the
same step of the timeline of the events and in an inter-temporal dimension. Fig. B.4
shows the comparison between the effective market discounts (shaped dots) and the
discounts estimated by the different agents while deleveraging. Expected discounts are
computed replacing the quantity of total assets sold in the market with the quantity
that the single banks is prepared to sell, namely using the sum at the numerator of
Eq. 12 in place of the quantity defining each strategy (the vector si in the notation
introduced above). The boxplots represent the distributions of the expected discounts
for the banks populating a stylized financial environment (see section 3 below) for six
selected asset classes. It is clear that even if the banks are informed on the market
depths they can hardly predict what will be the outcome of the strategy when the
effective discounts depend on the strategy of other banks. Notice that even strategies
trying to predict the market discounts using past values are likely to underestimate
the losses implied by market discounts, especially in the first stages of the crisis where
the great part of the losses imputed to the stress test are concentrated.

RWCR shift4.0e+081.0e+090.0050.0150.0256.0e+081.2e+094.0e+081.0e+090.10**Sold Assets−0.04 −0.51*** CB pledged1e+083e+085e+086.0e+081.0e+091.4e+090.0050.0200.00 −0.71***1e+084e+08−0.22***Repo pledgedECB Working Paper Series No 281459Figure B.4: A comparison of effective assets value discounts (shaped dots) with assets value dis-
counts expected by single banks (boxplot of the distribution) for six time steps and six selected assets
categories.

Local search with simple heuristics. We sketch in this paragraph a simple search
algorithm within the strategy space, building on the results by Coen et al. (2019).
Even though the simplifying assumptions of their work do not hold for the proposed
framework, we use their results as a reference point for a local exploration of the
strategy space of each bank. Formally, any bank finding herself in need of liquidity for
a quantity λ, accessing the available funding sources through the following steps

1. Collect all the disposable marketable and non-marketable assets (i.e. excluding

encumbered assets on assets that cannot be mobilized).

ket depths and the available amount

2. Order the assets i) by market depth (Dµ), ii) by the ratio between the mar-
, iii) by the risk-weighted ratio
(cid:17)48. Notice here that our orderings while defined for marketable

ρµ
assets, can also include non-marketable assets with null market depth.

1 + Dµ

(cid:16) Dµ

AM,une

AM,une

(cid:16)

(cid:17)

µ

µ

3. Given the liquidity need λ, define an allocation quantity for each asset class vµ

using the proportional deleveraging rule, i.e.

uµ(AM,une
µ

) =

uµ(AM,une
µ

) =

AM,une
µ
+ (cid:80)

(cid:80)

µ AM,une

µ

ν AN,une

ν

AM,une
µ
+ (cid:80)

(cid:80)

µ AM,une

µ

ν AN,une

ν

λ

λ

4. For any order defined at point 2, the bank takes that ordering and its reverse.
This defines six orderings of the asset classes. For any of these orderings, starting

48 Details on the rationale for this orderings can be found in Coen et al. (2019).

0.020.377.39123456Time stepsDiscounts (bps)Asset class: a1a2a3a4a5ECB Working Paper Series No 281460from the first asset class the quantity selected at point 3 is picked and a share at
random α uµ is sold in the market, while the remainder (1 − α) uµ is mobilized
to get credit against collateral. The bank chooses to borrow from the Central
Bank or in the private market comparing the haircuts and opting for the channel
where the liquidity for unit of collateral is higher. The bank stops when she gets
the needed liquidity λ or when the disposable assets are exhausted. This step
is implemented H times, where H defines the search depth, anytime selecting
different combination of α. Notice that for non-marketable assets α is set to zero
by default.

5. Collect all the strategies and selects the one with minimal equity loss. If many
strategies are equivalent according to the equity loss, then strategies with mini-
mal sold assets and minimal used assets are preferred.

ECB Working Paper Series No 281461Appendix C. Summary statistics

Tot. Asset (Bl)
Tot. Liabilities (Bl)
Equity (Bl)
CET1 (Bl)
CET1 ratio (%)
LCR (bp)
Leverage ratio (%)

Mean
278.01
260.61
17.40
15.38
16.93
235.32
6.70

SD
432.05
407.67
24.77
21.40
4.72
126.15
2.42

Min
3.92
3.52
0.24
0.21
11.12
123.94
4.02

25%
48.02
44.83
3.41
3.14
13.70
162.86
5.16

50%
90.96
81.90
6.27
5.85
15.73
196.42
5.94

75%
286.03
269.73
17.01
14.84
18.49
261.15
7.26

Max
2369.64
2247.27
122.37
100.26
36.28
946.05
15.50

Table C.1: Summary statistics for aggregate balance sheets. Source: authors
computations on supervisory data

Category Classification Type
Asset
Asset
Asset
Asset
Asset
Asset
Asset
Asset
Asset
Asset
Asset
Asset
Asset
Asset
Asset
Asset
Asset
Asset

Counterpart
Non-tradable Debt instruments Central bank
Non-tradable Debt instruments Credit institutions
Non-tradable Debt instruments Government
Non-tradable Debt instruments Non-financial institutions
Non-tradable Debt instruments Other financial institutions
Non-tradable Derivatives
Non-tradable Derivatives
Non-tradable Derivatives
Non-tradable Equity
Non-tradable Equity
Non-tradable Equity
Non-tradable Equity
Non-tradable Loans
Non-tradable Loans
Non-tradable Loans
Non-tradable Loans
Non-tradable Loans
Non-tradable Loans

Credit institutions
Other
Other financial institutions
Credit institutions
Non-financial institutions
Other
Other financial institutions
Central bank
Credit institutions
Government
Households
Non-financial institutions
Other financial institutions

Value (Bl) Share (%)
0.26
2.22
9.26
0.72
1.27
0.29
0.01
0.15
0.08
0.15
0.01
0.30
1.06
4.90
3.26
35.68
33.35
7.05

32.53
278.42
1159.88
90.50
159.22
35.79
1.73
19.01
9.05
19.36
1.29
37.83
131.79
614.04
408.91
4473.88
4182.21
883.60

Table C.2: Composition of non-tradable assets. Source: authors computations on
supervisory data

ECB Working Paper Series No 281462Category Classification Type
Asset
Tradable
Tradable
Asset
Tradable
Asset
Tradable
Asset
Tradable
Asset
Tradable
Asset
Tradable
Asset
Tradable
Asset
Tradable
Asset
Tradable
Asset
Tradable
Asset
Tradable
Asset
Tradable
Asset
Tradable
Asset
Tradable
Asset
Tradable
Asset
Tradable
Asset
Tradable
Asset

Counterpart
Debt instruments Central bank
Debt instruments Credit institutions
Debt instruments Government
Debt instruments Non-financial institutions
Debt instruments Other financial institutions
Derivatives
Derivatives
Derivatives
Equity
Equity
Equity
Equity
Loans
Loans
Loans
Loans
Loans
Loans

Credit institutions
Other
Other financial institutions
Credit institutions
Non-financial institutions
Other
Other financial institutions
Central bank
Credit institutions
Government
Households
Non-financial institutions
Other financial institutions

Value (Bl) Share (%)
0.16
1.32
12.45
1.73
1.37
26.40
8.92
13.80
0.84
8.01
0.01
1.93
1.55
8.50
0.59
0.03
2.10
10.31

3.67
29.65
279.25
38.76
30.69
592.03
200.00
309.55
18.85
179.59
0.24
43.38
34.70
190.49
13.35
0.47
47.09
231.09

Table C.3: Composition of tradable assets. Source: authors computations on
supervisory data

Credit institutions
Non-financial institutions
Other
Other financial institutions
Central bank
Credit institutions
Government
Households
Non-financial institutions
Other financial institutions

Category Classification Type
Asset
Asset
Asset
Asset
Asset
Asset
Asset
Asset
Asset
Asset
Asset
Asset
Asset
Asset
Asset
Asset
Asset
Asset
Asset
Asset
Asset
Asset
Asset
Asset
Asset
Asset
Asset
Asset
Asset

Counterpart
Non-tradable Debt instruments Central bank
Non-tradable Debt instruments Credit institutions
Non-tradable Debt instruments Government
Non-tradable Debt instruments Non-financial institutions
Non-tradable Debt instruments Other financial institutions
Non-tradable Equity
Non-tradable Equity
Non-tradable Equity
Non-tradable Equity
Non-tradable Loans
Non-tradable Loans
Non-tradable Loans
Non-tradable Loans
Non-tradable Loans
Non-tradable Loans
Tradable
Tradable
Tradable
Tradable
Tradable
Tradable
Tradable
Tradable
Tradable
Tradable
Tradable
Tradable
Tradable
Tradable

Debt instruments Central bank
Debt instruments Credit institutions
Debt instruments Government
Debt instruments Non-financial institutions
Debt instruments Other financial institutions
Equity
Equity
Equity
Equity
Loans
Loans
Loans
Loans
Loans

Credit institutions
Non-financial institutions
Other
Other financial institutions
Central bank
Credit institutions
Government
Households
Other financial institutions

Value (Bl) Share (%)
0.42
3.56
15.60
1.16
2.38
0.08
0.13
0.01
0.29
0.75
5.22
3.67
29.76
17.76
6.33
0.05
0.42
4.75
0.67
0.51
0.32
2.91
0.00
0.70
0.17
1.14
0.09
0.00
1.14

15.86
133.30
583.71
43.60
89.10
3.15
5.02
0.44
11.03
28.25
195.45
137.45
1113.79
664.55
236.88
1.82
15.57
177.73
25.10
19.11
11.83
108.80
0.07
26.12
6.27
42.75
3.42
0.12
42.52

Table C.4: Composition of encumbered assets. Source: authors computations on
supervisory data

ECB Working Paper Series No 281463Credit institutions
Non-financial institutions
Other
Other financial institutions
Central bank
Credit institutions
Government
Households
Non-financial institutions
Other financial institutions

Category Classification Type
Asset
Asset
Asset
Asset
Asset
Asset
Asset
Asset
Asset
Asset
Asset
Asset
Asset
Asset
Asset
Asset
Asset
Asset
Asset
Asset
Asset
Asset
Asset
Asset
Asset
Asset
Asset
Asset
Asset

Counterpart
Non-tradable Debt instruments Central bank
Non-tradable Debt instruments Credit institutions
Non-tradable Debt instruments Government
Non-tradable Debt instruments Non-financial institutions
Non-tradable Debt instruments Other financial institutions
Non-tradable Equity
Non-tradable Equity
Non-tradable Equity
Non-tradable Equity
Non-tradable Loans
Non-tradable Loans
Non-tradable Loans
Non-tradable Loans
Non-tradable Loans
Non-tradable Loans
Tradable
Tradable
Tradable
Tradable
Tradable
Tradable
Tradable
Tradable
Tradable
Tradable
Tradable
Tradable
Tradable
Tradable

Debt instruments Central bank
Debt instruments Credit institutions
Debt instruments Government
Debt instruments Non-financial institutions
Debt instruments Other financial institutions
Equity
Equity
Equity
Equity
Loans
Loans
Loans
Loans
Loans

Credit institutions
Non-financial institutions
Other
Other financial institutions
Central bank
Credit institutions
Government
Households
Other financial institutions

Value (Bl) Share (%)
0.17
1.48
5.86
0.48
0.71
0.06
0.15
0.01
0.27
1.05
4.26
2.76
34.17
35.77
6.58
0.02
0.14
1.03
0.14
0.12
0.07
0.72
0.00
0.18
0.29
1.50
0.10
0.00
1.92

16.67
145.12
576.17
46.90
70.12
5.90
14.34
0.85
26.80
103.54
418.59
271.46
3360.09
3517.66
646.72
1.85
14.08
101.52
13.66
11.58
7.02
70.79
0.17
17.26
28.43
147.74
9.93
0.35
188.57

Table C.5: Composition of unencumbered assets. Source: authors computations on
supervisory data

ECB Working Paper Series No 281464Country Value (Bl) Share (%)
1.58
185.11
AT
0.70
82.11
AU
3.84
448.62
BE
0.70
81.43
CA
0.61
70.94
CH
0.55
64.41
CN
0.11
12.53
CY
13.21
1545.48
DE
1.13
132.62
DK
0.05
6.06
EE
9.13
1067.81
ES
152.37
FI
1.30
12.36
1445.82
FR
8.79
1028.20
GB
1.18
137.68
GR
0.30
35.18
HK
1.37
159.90
IE
8.91
1041.96
IT
1.24
145.20
JP
0.43
50.01
KR
0.06
7.46
LT
1.66
193.74
LU
0.03
3.52
LV
0.05
6.02
MT
6.54
765.11
NL
0.67
78.54
NO
0.03
3.28
NZ
1.48
172.96
PT
33.14
RU
0.28
11.62
1359.27
RW
1.07
125.35
SE
0.37
42.81
SG
0.13
14.94
SI
0.54
62.58
SK
7.98
933.59
US

Table C.6: Composition of assets by country of counterpart (RW = Rest of the
World). Source: authors computations on supervisory data

ECB Working Paper Series No 281465Country Value (Bl) Share (%)
3.14
131.26
AT
0.25
AU
10.40
4.20
175.54
BE
0.35
14.48
CA
1.14
47.54
CH
0.07
2.85
CN
0.21
8.85
CY
13.46
562.98
DE
0.98
40.87
DK
0.11
4.80
EE
11.61
485.52
ES
2.82
117.96
FI
14.98
626.50
FR
4.05
169.23
GB
1.37
57.32
GR
0.38
15.92
HK
1.43
59.77
IE
12.73
532.45
IT
1.67
69.65
JP
0.06
2.46
KR
0.11
LT
4.62
2.76
115.51
LU
0.05
2.28
LV
0.06
2.35
MT
8.63
360.85
NL
0.13
5.57
NO
0.00
0.12
NZ
1.65
69.01
PT
0.30
RU
12.51
4.33
180.98
RW
0.41
17.10
SE
0.28
11.53
SG
0.24
10.06
SI
0.64
26.93
SK
5.41
226.41
US

Table C.7: Composition of loans to non-financial corporations by country of
counterpart (RW = Rest of the World). Source: authors computations on AnaCredit

ECB Working Paper Series No 281466Prob. of default Value (Bl) Share (%)
83.16
<0.1
2.16
>=0.1 and <0.4
3.20
>=0.4
11.48
ND

3477.82
90.39
134.00
479.99

Table C.8: Composition of loans to non-financial corporations by probability of
default. Source: authors computations on AnaCredit

Maturity
<3 years
>=3 and <7 years
>=7 years

Value (Bl) Share (%)
47.74
24.40
27.86

1996.55
1020.58
1165.09

Table C.9: Composition of loans to non-financial corporations by maturity. Source:
authors computations on AnaCredit

ECB Working Paper Series No 281467NACE Code (Lv.2) Description
1
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24
25
26
27
28
29
30
31
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33
35
36
37
38
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41
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45
46
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91
92
93
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95
96
97
98
99

Crop and animal production, hunting and related service activities
Forestry and logging
Fishing and aquaculture
Mining of coal and lignite
Extraction of crude petroleum and natural gas
Mining of metal ores
Other mining and quarrying
Mining support service activities
Manufacture of food products
Manufacture of beverages
Manufacture of tobacco products
Manufacture of textiles
Manufacture of wearing apparel
Manufacture of leather and related products
Manufacture of wood and of products of wood and cork, except furniture; manufacture of articles of straw and plaiting materials
Manufacture of paper and paper products
Printing and reproduction of recorded media
Manufacture of coke and refined petroleum products
Manufacture of chemicals and chemical products
Manufacture of basic pharmaceutical products and pharmaceutical preparations
Manufacture of rubber and plastic products
Manufacture of other non-metallic mineral products
Manufacture of basic metals
Manufacture of fabricated metal products, except machinery and equipment
Manufacture of computer, electronic and optical products
Manufacture of electrical equipment
Manufacture of machinery and equipment n.e.c.
Manufacture of motor vehicles, trailers and semi-trailers
Manufacture of other transport equipment
Manufacture of furniture
Other manufacturing
Repair and installation of machinery and equipment
Electricity, gas, steam and air conditioning supply
Water collection, treatment and supply
Sewerage
Waste collection, treatment and disposal activities; materials recovery
Remediation activities and other waste management services
Construction of buildings
Civil engineering
Specialised construction activities
Wholesale and retail trade and repair of motor vehicles and motorcycles
Wholesale trade, except of motor vehicles and motorcycles
Retail trade, except of motor vehicles and motorcycles
Land transport and transport via pipelines
Water transport
Air transport
Warehousing and support activities for transportation
Postal and courier activities
Accommodation
Food and beverage service activities
Publishing activities
Motion picture, video and television programme production, sound recording and music publishing activities
Programming and broadcasting activities
Telecommunications
Computer programming, consultancy and related activities
Information service activities
Financial service activities, except insurance and pension funding
Insurance, reinsurance and pension funding, except compulsory social security
Activities auxiliary to financial services and insurance activities
Real estate activities
Legal and accounting activities
Activities of head offices; management consultancy activities
Architectural and engineering activities; technical testing and analysis
Scientific research and development
Advertising and market research
Other professional, scientific and technical activities
Veterinary activities
Rental and leasing activities
Employment activities
Travel agency, tour operator and other reservation service and related activities
Security and investigation activities
Services to buildings and landscape activities
Office administrative, office support and other business support activities
Public administration and defence; compulsory social security
Education
Human health activities
Residential care activities
Social work activities without accommodation
Creative, arts and entertainment activities
Libraries, archives, museums and other cultural activities
Gambling and betting activities
Sports activities and amusement and recreation activities
Activities of membership organisations
Repair of computers and personal and household goods
Other personal service activities
Activities of households as employers of domestic personnel
Undifferentiated goods- and services-producing activities of private households for own use
Activities of extraterritorial organisations and bodies

Value (Bl) Share (%)
1.19
0.06
0.04
0.01
0.32
0.09
0.09
0.10
1.62
0.30
0.03
0.21
0.15
0.12
0.25
0.35
0.12
0.35
0.71
0.29
0.48
0.41
0.70
0.96
0.43
0.43
0.87
1.01
0.36
0.14
0.26
0.37
3.37
0.22
0.11
0.26
0.01
2.56
0.53
0.94
1.21
5.16
2.34
1.04
0.76
0.26
1.14
0.23
1.40
0.66
0.21
0.11
0.04
0.66
0.57
0.16
24.83
2.81
3.12
14.37
0.30
5.99
0.42
0.09
0.13
0.24
0.02
1.87
0.10
0.13
0.04
0.16
1.14
0.15
0.20
0.74
0.30
0.09
0.04
0.04
0.07
0.26
0.10
0.02
0.25
0.01
0.00
0.04

49.68
2.53
1.82
0.41
13.33
3.84
3.96
4.10
67.56
12.57
1.05
8.85
6.09
4.90
10.25
14.44
5.14
14.75
29.88
12.24
19.97
17.11
29.24
40.23
17.82
18.17
36.41
42.29
15.06
5.74
10.87
15.53
141.14
9.25
4.72
10.94
0.59
106.94
22.31
39.32
50.55
215.76
98.02
43.57
31.96
11.06
47.53
9.66
58.58
27.61
8.72
4.57
1.68
27.41
23.82
6.63
1038.52
117.57
130.28
600.88
12.47
250.32
17.70
3.88
5.44
10.20
0.90
78.28
4.35
5.27
1.79
6.85
47.71
6.25
8.25
30.84
12.44
3.67
1.74
1.63
2.74
10.97
4.37
0.67
10.58
0.22
0.09
1.58

Table C.10: Composition of loans to non-financial corporations by economic sector.
Source: authors computations on AnaCredit

ECB Working Paper Series No 281468Counterpart
Central bank
Credit institutions
Households
Non-financial institutions
Other finanacial institutions

Category Type
Liability Debt instruments
Liability Deposit
Liability Deposit
Liability Deposit
Liability Deposit
Liability Deposit (agreed maturity) Households
Liability Government
Liability Other
Liability Repo
Liability
Liability Unsecured

Secured

Deposit

Debt instruments

Value (Bl) Share (%)
9.04
1.53
26.65
14.18
4.38
3.04
2.33
13.14
4.20
6.65
14.86

1595.25
270.47
4702.59
2502.15
772.63
535.95
411.34
2318.93
741.05
1173.83
2623.03

Table C.11: Composition of liabilities. Source: authors computations on supervisory
data

ECB Working Paper Series No 281469Appendix D. Data references

Counterpart
Total

Category Classification Type
Finrep reference
Asset
Non-tradable Cash
F_20.04_10_75 - F_20.04_11_75
F_20.04_10_90 - F_20.04_11_90
Non-tradable Debt instruments Central bank
Asset
F_20.04_10_110 - F_20.04_11_110
Non-tradable Debt instruments Credit institutions
Asset
F_20.04_10_100 - F_20.04_11_100
Non-tradable Debt instruments Government
Asset
Non-tradable Debt instruments Non-financial institutions
Asset
F_20.04_10_130 - F_20.04_11_130
Non-tradable Debt instruments Other financial institutions F_20.04_10_120 - F_20.04_11_120
Asset
Non-tradable Debt instruments Total
Asset
Non-tradable Derivatives
Asset
Non-tradable Derivatives
Asset
Non-tradable Derivatives
Asset
Non-tradable Equity
Asset
Non-tradable Equity
Asset
Non-tradable Equity
Asset
Non-tradable Equity
Asset
Non-tradable Loans
Asset
Non-tradable Loans
Asset
Non-tradable Loans
Asset
Non-tradable Loans
Asset
Non-tradable Loans
Asset
Non-tradable Loans
Asset
Non-tradable Loans
Asset
Tradable
Asset
Tradable
Asset
Tradable
Asset
Tradable
Asset
Tradable
Asset
Tradable
Asset
Tradable
Asset
Tradable
Asset
Tradable
Asset
Tradable
Asset
Tradable
Asset
Tradable
Asset
Tradable
Asset
Tradable
Asset
Tradable
Asset
Tradable
Asset
Tradable
Asset
Tradable
Asset
Tradable
Asset
Tradable
Asset

F_20.04_10_80 - F_20.04_11_80
Credit institutions
F_20.04_10_20 - F_20.04_11_20
Other financial institutions F_20.04_10_30 - F_20.04_11_30
F_20.04_10_10 - F_20.04_11_10
Total
Credit institutions
F_20.04_10_50 - F_20.04_11_50
F_20.04_10_70 - F_20.04_11_70
Non-financial institutions
Other financial institutions F_20.04_10_60 - F_20.04_11_60
F_20.04_10_40 - F_20.04_11_40
Total
F_20.04_10_150 - F_20.04_11_150
Central bank
F_20.04_10_170 - F_20.04_11_170
Credit institutions
F_20.04_10_160 - F_20.04_11_160
Government
F_20.04_10_220 - F_20.04_11_220
Households
Non-financial institutions
F_20.04_10_190 - F_20.04_11_190
Other financial institutions F_20.04_10_180 - F_20.04_11_180
F_20.04_10_140 - F_20.04_11_140
Total
F_20.04_11_90
Debt instruments Central bank
F_20.04_11_110
Debt instruments Credit institutions
F_20.04_11_100
Debt instruments Government
Debt instruments Non-financial institutions
F_20.04_11_130
Debt instruments Other financial institutions F_20.04_11_120
F_20.04_11_80
Debt instruments Total
Credit institutions
Derivatives
F_20.04_11_20
Other financial institutions F_20.04_11_30
Derivatives
F_20.04_11_10
Total
Derivatives
F_20.04_11_50
Credit institutions
Equity
Non-financial institutions
Equity
F_20.04_11_70
Other financial institutions F_20.04_11_60
Equity
F_20.04_11_40
Total
Equity
F_20.04_11_150
Central bank
Loans
F_20.04_11_170
Credit institutions
Loans
F_20.04_11_160
Government
Loans
F_20.04_11_220
Households
Loans
Non-financial institutions
Loans
F_20.04_11_190
Other financial institutions F_20.04_11_180
Loans
F_20.04_11_140
Total
Loans

Table D.1: Finrep references for assets

ECB Working Paper Series No 2814700
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ECB Working Paper Series No 281472Acknowledgements 

This paper results from a long process that beneﬁted from helpful comments over time. The authors thank G. Camba-Mendez, K. Kok, 
S. Scheﬄer and an anonymous referee for their valuable suggestions. We are also indebted to colleagues who participated in the 2022 
Sant’Anna PhD Workshop, the DGMF Seminar Series, and the ECB 2022 Research Workshop organised by the Working Group on 
Stress Testing for insightful discussions. 
This paper should not be reported as representing the European Central Bank’s (ECB) views. The opinions expressed are those of the 
authors and do not necessarily reﬂect those of the ECB. 

Angelo Cuzzola 
Scuola Superiore Sant’Anna, Pisa, Italy; email: Angelo.Cuzzola@santannapisa.it 

Claudio Barbieri 
European Central Bank, Frankfurt am Main, Germany; Université Côte d’Azur, Nice, France; email: Claudio.Barbieri@ecb.europa.eu 

Ulrich Bindseil 
European Central Bank, Frankfurt am Main, Germany; email: Ulrich.Bindseil@ecb.europa.eu 

© European Central Bank, 2023 

Postal address  60640 Frankfurt am Main, Germany 
Telephone 
Website 

+49 69 1344 0 
www.ecb.europa.eu 

All rights reserved. Any reproduction, publication and reprint in the form of a different publication, whether printed or produced 
electronically, in whole or in part, is permitted only with the explicit written authorisation of the ECB or the authors.  

This paper can be downloaded without charge from www.ecb.europa.eu, from the Social Science Research Network electronic library or 
from RePEc: Research Papers in Economics. Information on all of the papers published in the ECB Working Paper Series can be found 
on the ECB’s website. 

PDF 

ISBN 978-92-899-6077-9 

ISSN 1725-2806 

doi:10.2866/910554  

QB-AR-23-051-EN-N