Multi-layered interbank model for assessing
systemic risk
Abstract
In this paper, we develop an agent-based multi-layered interbank net-
work model based on a sample of large EU banks. The model allows for
taking a more holistic approach to interbank contagion than is standard
in the literature. A key finding of the paper is that there are material
non-linearities in the propagation of shocks to individual banks when tak-
ing into account that banks are related to each other in various market
segments. The contagion effects when considering the shock propaga-
tion simultaneously across multiple layers of interbank networks can be
substantially larger than the sum of the contagion-induced losses when
considering the network layers individually. In addition, a bank “systemic
importance” measure based on the multi-layered network model is devel-
oped and is shown to outperform. standard network centrality indicators.
The finding of non-linear contagion effects when accounting for the inter-
action between the different layers of banks’ interlinkages have important
policy implications. For example, it provides an argument for separating
banks’ trading activities from their other intermediation activities.
JEL Classification: C45, C63, D85, G21
Key words: Financial contagion, interbank market, network theory
ECB Working Paper 1944, August 2016 1
Non-technical summary
In this paper, we develop an agent-based multi-layered interbank
network model based on a sample of large EU banks. The model
allows for taking a more holistic approach to interbank contagion
than is standard in the literature, where bank-to-bank spillover ef-
fects are typically confined to specific segments. However, in reality
banks are interrelated in several dimensions of their business activi-
ties. Thebasicnotionpromotedinthepaperisthatunlesscontagion
risk across the many layers of interrelations between banks are taken
into account, it is likely that contagion effects will be substantially
underestimated.
Specifically, in this paper we consider three different layers of
interbank relationships. These include a network of short-term in-
terbank loans (i.e. less than 3-month maturity) to reflect funding
risk and a network of longer-term bilateral exposures (i.e. above
3-month maturity) to reflect counterparty risk. In addition, we con-
sider a third network layer of common exposures in banks’ securities
portfolios where contagion can spread when one bank is forced to
sell those securities that may give rise to sharp revaluation effects.
This last layer aims at capturing market risk.
On top of the multi-layered system we put an agent-based model
whereagentscaninteractwitheachotherthroughthenetworkstruc-
ture. The introduction of agents enables us to investigate specific
network structures in combination with plausible bank behaviors.
In particular, in the model banks only adjust their balance sheets
when endogenous or exogenous shocks bring their liquidity or their
risk-weighted capital ratio below the minimum requirements.
Our dataset include a sample of 50 large EU banks. For each
bank, we include information about capital, short-term and long-
term interbank borrowing, deposits, short-term and long-term in-
terbank loans, aggregate securities holdings, and cash. We do not
have data on individual banks bilateral exposures, neither on the
details of financial securities portfolios. Instead, we use this uncer-
tainty as degree of freedom of the model, in order to investigate
which multi-layered network structures are particularly prone to a
systemic breakdown.
Akeyfindingofthepaperisthattherearematerialnon-linearities
in the propagation of shocks to individual banks when taking into
account that banks are related to each other in various market seg-
ments. In a nutshell, the contagion effects when considering the
shockpropagationsimultaneouslyacrossmultiplelayersofinterbank
networks can be substantially larger than the sum of the contagion-
ECB Working Paper 1944, August 2016 2
induced losses when considering the network layers individually. In
addition, abank“systemicimportance”measurebasedonthemulti-
layered network model is developed and is shown to outperform
standard network centrality indicators.
The finding of non-linear contagion effects when accounting for
the interaction between the different layers of banks’ interlinkages
have important policy implications. For example, it provides an
argument for separating banks’ trading activities from their other
intermediation activities.
ECB Working Paper 1944, August 2016 3
1 Introduction
During the financial crisis that emerged in 2008 a large part of the
global financial system came under stress with severe repercussions
on the real economy.
A robust financial system should not amplify the propagation of
idiosyncratic (or “local”) shocks to other parts of the system and
ultimately to the real economy. In this paper, systemic risk exactly
refers to the possibility that the financial system is in a configu-
ration which makes it particularly prone to global breakdowns in
case of an initial, local shock. The reasons driving the system to
such unstable and fragile configurations are probably rooted in the
duality among local and global properties of the financial system.
As a matter of fact, each financial institution takes actions with the
aim of maximizing its own profits and interests, while the impact of
those actions on the stability of the system as a whole are hardly
taken into account. Moreover, as we will show in this paper, also if
banks were willing to minimize systemic risk when they take deci-
sions, they would need to have sufficient information regarding the
financial situations of the other banks, including the exposures each
bank have on all the others. As an example, one can consider the
direct exposures in an interbank market. If one bank wants to eval-
uate the riskiness associated with a loan to another bank, it should
be able to know the exposures of its counterparty, which probability
of default depends on its own counterparties, and so on. No bank is
able to peer so deeply into the interbank credit network to evaluate
the probability of defaults due to contagion effects.
A crucial role in ensuring financial stability is therefore played
by information. If the ultimate goal is to reduce systemic risk, it
is necessary to have a global view of the financial system in order
to identify and monitor possible sources and channels of contagion.
A robust framework for monitoring and assessing financial stability,
and for managing it with interventions able to prevent the system
from entering into critical configurations, must be able to evaluate
the continuously evolving structure of the financial system.
Another important lesson emerging from the recent financial cri-
sisthatwetrytoaccountforinthispaperisthatthepossiblesources
of systemic instability are multiple. For instance, direct bilateral ex-
posures can create domino effects and propagate idiosyncratic (or
local) shocks to the wider (global) financial system. In addition,
institutions can be forced to sell part of their security portfolios.
This can lead to strong asset price declines and can transmit losses
through banks with common exposures and overlapping portfolios.
ECB Working Paper 1944, August 2016 4
Furthermore, news about a firm’s assets can signal that others with
similar assets may also be distressed and thus create widespread
market uncertainty. Moreover, the sudden interruption of a service
provided by a bank to the financial system can constitute a threat in
case other banks are not able to immediately substitute it. When all
those dynamics work together, the result can be critical, although
the initial shock was comparably small.
Against this background, the aim of this paper is to study sys-
temic risk in highly interconnected financial systems. A natural way
torepresentandstudyaninterbankmarketisnetworktheory, nowa-
days commonly used in finance. In order to encapsulate the different
kinds of possible connections among banks, we use a multi-layered
network model. A multi-layered network is a system where the same
setofnodesbelongtodifferentlayers, andeachlayerischaracterized
by its own kind of edge (representing a particular kind of financial
connection), by its own topology (so each node may have different
neighbors in different layers), and its own rules for the propagation
of eventual shocks. This holistic view of the financial system should
enable us to study systemic risk in a more encompassing perspec-
tive, than the typical single-layered network structures focusing on
individual segments.
On top of the multi-layered system we put an agent-based model
where agents can interact with each other through the network
structure. The standard approach in the literature to study sys-
temic risk using network theory represents banks as passive entities
(the nodes of the network) connected to each other by some kind
of financial contract, generally being interbank loans (the edges of
the network).1 Those kinds of models are good at estimating the
resilience of particular network structures against shocks, but they
lack real dynamic effects, since shocks propagate through the system
without incorporating the (likely) reaction of banks to those shocks.
The introduction of agents enable us to investigate specific network
structures in combination with a plausible bank behavior. In partic-
ular, in our model banks will only adjust their balance sheets when
endogenous or exogenous shocks bring their liquidity or their risk-
weighted capital ratio below the minimum requirements. In fact, if
we assume that prior to the shock the system was in equilibrium,
banks would just try to keep the same structure of their balance
sheets also during the propagation of the shock.
The failure of a financial institution usually implies several reper-
cussions on the system. The liquidation of a failed bank can push
1A pioneering work in this direction was initially proposed by Nier et al. (2009), while a
summary of the results coming from this branch of literature can be found in Upper (2011).
ECB Working Paper 1944, August 2016 5
prices down, its counterparts can book losses from direct exposures,
the financial services provided by that bank cannot always be re-
placed, at least not immediately, and the combination of such re-
actions can significantly amplify shocks and lead to dangerous spi-
rals which could potentially collapse a substantial part of the finan-
cial system (Brunnermeier (2009)). The complete dynamics of such
events is difficult to capture with analytical models and from this
perspective an agent-based model is more suitable, since it enables
studying also systems out of equilibrium.
The agent-based model combined with the multi-layered network
representation of the financial system is subsequently used to design
measures for the systemic importance of each bank in the system.
Those measures rely on information regarding direct and indirect
interbank connections, which can be inferred from network theory,
and banks’ balance sheet information. The basic notion is that stan-
dard network centrality measures alone cannot explain the systemic
importance of individual financial institutions, since the high level
of heterogeneity in banking systems can bring central capitalized
nodes to stabilize the system, whereas network measures would just
judge nodes depending on their centrality. Instead, it is necessary
to combine information regarding the balance sheet structure of in-
stitutions with measures of centrality in order to understand the
impact of each bank failure on the system.
This paper is organized as follows: section 2 reviews the main
literature linked to our work, highlighting both the contributions
in the multi-layered network theory and the agent-based interbank
models; section 3 introduces the multi-layered interbank market and
explains how the structure is calibrated on a real dataset; section
4 explains the model we use for investigating systemic risk; section
5 presents details about the implementation of the model and the
resultsfromoursimulationengine; section6introducesourmeasures
for the systemic importance banks, and shows how the measures can
be used to monitor systemic risk in the system; section 7 concludes
and provides some policy implications.