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168 Journal of Risk Management in Financial Institutions Vol. 12, 2 168–183 © Henry Stewart Publications 1752-8887 (2019)
Interconnectedness and
financial stability
Received (in revised form) 14th February, 2019
Serafin Martinez-Jaramillo
is a senior financial researcher at the Financial Stability General Directorate at Banco de México and he is currently an adviser at the
CEMLA. His research interests include financial stability, systemic risk, financial networks, bankruptcy prediction, genetic programming,
multiplex networks and machine learning. Serafin has published book chapters, encyclopedia entries and papers in several journals,
such as the IEEE Transactions on Evolutionary Computation, Journal of Financial Stability, Neurocomputing, Journal of Economic
Dynamics and Control, Computational Management Science, Journal of Network Theory in Finance and others. Additionally, he has
co-edited two books and two special issues for the Journal of Financial Stability. Serafin holds a PhD in computational finance from
the University of Essex, UK and he is member of the editorial board of the Journal of Financial Stability and the Journal of Network
Theory in Finance.
Centro de Estudios Monetarios Latinoamericanos, Durango 54, Colonia Roma Norte, Delegación Cuauhtémoc, C.P. 06700,
Ciudad de México, México; and Banco de Mexico, Avenida 5 de Mayo 2, Colonia Centro, Código postal 06000, Delegación
Cuauhtémoc, Ciudad de México, México
E-mail: smartin@banxico.org.mx
Christian U. Carmona
is a doctoral candidate reading statistics at the University of Oxford. His research interests are mainly concentrated in applied
probabilistic modelling, Bayesian inference and the study of relational data. Before Oxford, he finished a master’s degree in statistics at
UC Berkeley, and worked for the Central Bank of Mexico building quantitative tools for financial risk management.
Department of Statistics, University of Oxford, 24–29 St Giles’, Oxford, OX1 3LB, UK
Dror Y. Kenett
is a multidisciplinary financial economist, an expert on financial networks, financial stability and systemic risk. He
isinternationallyrenownedfor his expertise onnetwork-based models, financial contagion and correlation-based models. He has
published more than 40 papers in financial, physics and engineering journals, such as the Journal of Banking and Finance, Journal of
Risk and Financial Management, Quantitative Finance, Nature Physics and Scientific Reports. He has a PhD in physics from Tel-Aviv
University, Israel.
Johns Hopkins University, Applied Economics, 1717 Massachusetts Ave., Washington, DC 20036, USA; and The London School of
Economics and Political Science, Systemic Risk Centre, Houghton Street, London, WC2A 2AE, UK
Abstract The 2007–2008 global financial crisis has been associated with a high level of connectivity
in the global financial system. The crisis, and the following events of the past decade, have highlighted
the relevance of the concept of interconnectedness to understanding systemic risk, transmission of
financial contagion and ultimately on the subject of financial stability. Nevertheless, the more general
relationship, across its full spectrum, between interconnectedness and financial stability, is still not
fully studied and understood. This paper reviews the positive aspects as well as the negative
aspects of interconnectedness. It also discusses briefly the important question of the optimal level
of connectivity in a financial system. Finally, the paper proposes the use of novel statistical inferential
methods for complex networks to address comprehensively the study of interconnectedness in
financial systems.
Keywords: interconnectedness, financial stability, statistical network models
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© Henry Stewart Publications 1752-8887 (2019) Vol. 12, 2 168–183 Journal of Risk Management in Financial Institutions 169
INTRODUCTION
The 2007–2008 Global Financial Crisis (GFC) has
revealed that existing tools and models were not
adequate to monitor effectively endogenous risks
arising within the highly interconnected network of
the global financial system. The failure of financial
institutions, particularly during the GFC has given rise
to fear regarding the possibility of a future domino-
style systemic collapse triggered by a failure of a
central entity. This has fostered several policy debates
and academic research on financial contagion, and
specifically regarding the issue of ‘too-interconnected-
to-fail’. While this aspect of interconnectedness,
which can be considered as a negative outcome, has
been widely studied, the positive aspects have received
much less attention. In this paper, we aim to provide
a comprehensive overview of the subject of financial
interconnectedness, by discussing both negative and
positive aspects. We go further by augmenting this
discussion with the question of whether there exists an
optimal level of interconnectedness. Finally, we end
the review by discussing two of the current leading
trends in the study of interconnectedness: the study
of multilayer financial networks, and the use of novel
statistical inference models.
Following the GFC and its fallout, financial
stability has been made a priority in almost all
national jurisdictions. Despite all the events and
fallouts since 2008, there is still no widely agreed
upon definition for the concept of financial stability.
The term has been defined in many ways by
different authorities and academics. For example, the
Board of Governors of the Federal Reserve System
defines it in the following way:
Financial stability is about building a financial system
that can function in good times and bad, and can
absorb all the good and bad things that happen in
the U.S. economy at any moment; it isn’t about
preventing failure or stopping people or businesses
from making or losing money. It is just helping to
create conditions where the system keeps working
effectively even with such events.1
In contrast, the European Central Bank has proposed
an alternative definition:
Financial stability can be defined as a condition in
which the financial system — which comprises
financial intermediaries, markets and market
infrastructures — is capable of withstanding shocks
and the unravelling of financial imbalances. This
mitigates the prospect of disruptions in the financial
intermediation process that are severe enough to
adversely impact real economic activity.2
From either alternative definitions presented above,
it is still not clear how interconnectedness and
financial stability are related. Moreover, there is no
mention in any of the above definitions regarding
the issue of connectivity, networks, contagion or any
related terminology.
In contrast, one can derive a very different view
of the concept of systemic risk, such as the one that
has been proposed for example by the Systemic Risk
Centre (SRC) at the London School of Economics.3
According to the SRC, systemic risk is defined in
the following way:
Systemic risk refers to the risk of a breakdown of
an entire system rather than simply the failure of
individual parts. In a financial context, it captures
the risk of a cascading failure in the financial sector,
caused by interlinkages within the financial system,
resulting in a severe economic downturn.
In this definition, there are two relevant terms
that are worth highlighting: cascading failure and
interlinkages. Therefore, according to this approach,
systemic risk is the risk of not having financial
stability and it involves both f inancial contagion
and interconnectedness. This is the main reason
why network theory and models have been widely
used to develop systemic risk models and analytics.
Furthermore, out of these has emerged what is now
referred to commonly in the financial jargon as ‘too
interconnected to fail’ — a term that refers to the
characteristic of certain institutions as being central
players in the financial network, whose failure could
threaten the functioning of the financial system as a
whole.
Connectivity is also considered to be closely
related to the stability of the financial system. This
stems from the hypothesis that financial connectivity
can provide a means for risk sharing among the
connected financial institutions, which results in
increased stability of the system as a whole. In this
regard, connectivity among financial institutions has
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become an integral part of macroprudential policies
such as stress testing.4 System-wide stress testing
is now part of the financial authorities’ toolkit
and in many cases involves second order effects
and contagion effects. This has led to a growing
interest in the topic across the financial system,
from academics, to regulators and practitioners;
however, this interest has mainly focused on the
issue of the risks, or transmission channels, that arise
from interconnectedness. While this is a natural and
dominant feature of connectivity, other important
features require more attention to reach a full
understanding of the nature of interconnectedness in
the financial system.
Moreover, network models provide the means
for combining both microprudential analysis and
policies, with macroprudential analysis and policies.
This is achieved by considering both the individual
counterparties in the network, and the relationships
between them that results in the network structure.
As such, network models have been used to study
how subsets of the financial system interact across
different activities; for example, on the one hand,
by considering interbank networks (eg see refs5,6),
or by studying specific financial activity and
the institutions involved in it. On the other hand,
the payment system7 or flow of collateral8 can be also
considered. These two complementary aspects can
be combined into a single comprehensive framework
using recent advances in network models arising
from the study of multilayer networks. This class
of networks provides the framework to study more
than one network in a single model.
Investigating the underlying structure of
connectivity is a challenging endeavour. Signif icant
insights have been attained by studying topological
features of an observed network generated by real-
world financial systems. Nevertheless, few attempts
have been made to fully characterise in a probabilistic
model the dynamic structure of the system. Recent
advances at the intersection of statistical modelling
and network science are clearing the path towards
comprehensive unified network models.
The rest of the paper is organised as follows:
in the next section we reflect on the better-
known research on the potential negative aspects
that result from interconnectedness, while in the
following section we present some arguments
on why interconnectedness is beneficial for the
financial system. Next, we discuss the issue of
whether there is an optimal degree of connectivity
for a financial system. The subsequent two sections
present novel tools that have recently been used to
study interconnectedness. The paper ends with our
conclusions.
DOES INTERCONNECTEDNESS
RESULT IN FINANCIAL FRAGILITY?
The concept of final interconnectedness has been
mostly associated with financial contagion, risk and
financial fragility. While earlier work on transmission
of risk through interconnectedness exists, for example,
Eisenberg and Noe’s model,9 this topic has become
a subject of key interest following the recent global
financial crisis. For example, Gai and Kapadia proposed
an analytical model of contagion in financial networks
that have an arbitrary structure,10 and Acemoglu
et al. have proposed a framework for studying the
relationship between the financial network architecture
and the likelihood of systemic failures owing to
contagion of counterparty risk.11 In a more recent
paper, Glasserman and Young12 review the extensive
literature on this issue, with the focus on how network
structure interacts with other key economic variables
that are considered to be related to the spread of shocks
and contagion. In their review, the authors discuss
various metrics that have been proposed for evaluating
the susceptibility of the system to contagion and
suggest directions for future research.
Battiston and Martinez-Jaramillo provide a recent
overview on the literature on network models for
financial contagion.13 The authors illustrate some of
the insights network models have to offer both in
terms of new fundamental scientific understanding of
the emergence systemic risk and in terms of concrete
applications to the policy areas of financial stability
and macroprudential policy. For example, some of
the topics discussed by the authors include the use
of network models to understand better the issue of
systemic risk in credit default swaps’ markets,14–16
the determination of the systemic importance of
financial institutions using network models17 and
on reconstruction methods that can be used when
only partial information of the financial networks is
available,18 among other relevant works. The common
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factor in many of the works surveyed by Battiston
and Martinez-Jaramillo13 is that interconnectedness in
general conveys higher systemic risk. These different
threads of research all share the use of network
models to study how shocks spread throughout the
financial system, and how they could potentially
be amplified as a result of the level and extent of
interconnectedness embedded in the system.
In particular, Roukny et al.19 study how the
network structure of the interbank credit market
introduces uncertainty to the determination of the
individual default probabilities of banks, therefore
affecting the estimation of systemic risk. This
result has important implications for systemic
risk measurement, given that interconnectedness
introduces an important source of complexity in the
computation of system-wide expected losses.
To conclude this section, an additional work that
is important to the discussion of the negative aspects
of higher f inancial connectivity on financial stability
is a paper by Constantin et al.20 In this paper, the
authors use information on the structure of the
financial network to predict banks distress. The
proposed model outperforms similar models that
do not use network information.
In summary, in this section we have reviewed
some of the vast and rapidly growing literature that
that discusses how the issues of interconnectedness
and financial stability are closely tied. The papers
mentioned above, and others, highlight the various
aspects that make the study of interconnectedness,
and network models more broadly, relevant for
systemic risk analysis, even beyond the single issue
of financial contagion.
IS INTERCONNECTEDNESS
BENEFICIAL FOR THE FINANCIAL
SYSTEM?
Andrew Haldane, Chief Economist at the Bank of
England, is famous for having suggested that:
highly interconnected financial networks may be
robust-yet-fragile in the sense that within a certain
range, connections serve as shock-absorbers [and]
connectivity engenders robustness. However, beyond
a certain range, interconnections start to serve as a
mechanism for the propagation of shocks, the system
[flips to] the wrong side of the knife-edge, and
fragility prevails.21
Nevertheless, while the fragility that can emerge from
interconnectedness has received significant attention
since the 2008 crisis (see eg ref. 12), the robustness
angle has received much less attention. In fact, as has
been shown in other domains, interconnections can
offer stability, risk sharing, knowledge transfer and
even recovery. In this section we discuss some recent
work that highlights some of the benefits that arise
from interconnectedness.
First, we review a recent theoretical paper
that proposed the benefits that emerge from
interconnectedness, in terms of the spread of recovery
in a network setting. A theoretical framework to
investigate both fragility and robustness that can
stem from interconnectedness has been proposed
by Majdandzic et al.22 The proposed framework
focuses on the dynamical processes that happen on
the network, resulting from the network structure,
and the abrupt dynamic events that cause networks
to irreversibly fail. In many real-world phenomena,
such as brain seizures in neuroscience or sudden
market crashes in finance, after such significant
network failure events, a significant part of the
damaged network is capable of spontaneously
becoming active again through a recovery process.
The process often occurs repeatedly, and a regime
switching phenomenon occurs between a failed state
of the network and a healthy state of the network. To
model this process of network recovery, Majdandzic
et al.22 examined the effect of local node recoveries
and stochastic contiguous spreading, and found
that they can lead to the spontaneous emergence
of macroscopic ‘phase f lipping’ phenomena. As the
network is of finite size and is stochastic, the fraction
of active nodes, which they define as z, switches back
and forth between the two network collective modes
characterised by high network activity and low
network activity. The model assumes that: (1) each
node in the network has an endogenous independent
probability of failure, as well as an endogenous
independent probability of recovery; (2) each node
in the network has an exogenous probability of
failure, resulting from what is considered ‘damage
connectivity’, stemming from being connected to
a number of failed nodes above a given threshold;
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and (3) each node in the network has an exogenous
probability of recovery, resulting from what is
considered ‘healthy connectivity’, stemming from
being connected to a number of recovered nodes
above a given threshold. Resulting from these
endogenous and exogenous probabilities of failure
and recovery, the network model exhibits regime
switching between a state where a majority of nodes
are active (or healthy) to one where a majority of
nodes are inactive (or damaged). Conceptually, the
model describes the effect of recovery contagion,
and how individual node recovery can contribute to
recovery of the system as a whole, resulting from the
network structure and interconnectedness. Using a
sample of stock returns from the US and Indian stock
markets, the authors show that when considering
the ratio of positive to negative stock returns of
individual stocks, one can observe qualitatively the
dynamic phenomenon that the model predicts.
As a second example, in a recent paper, Di Muro
et al. have proposed an analytic and numerical
framework for studying the concurrent failure and
recovery of a system of interdependent networks.23
Thus, while the previous example discussed the role
that a recovery process can play in the dynamics of a
system, this example discusses a strategy of inducing
recovery into the system, after the onset of some
stress to the system. The framework consists of
repairing a fraction of failed nodes, with probability
of recovery, that are neighbours of the largest
connected component of each constituent network.
The authors find that for a given initial failure of
a fraction of nodes, there is a critical probability of
recovery above which the cascade is halted and the
system fully restores to its initial state and below
which the system abruptly collapses.
Third, Rogers and Veraart24 model the interbank
market as a network, building on the modelling
paradigm of Eisenberg and Noe,9 and extending it
by introducing default costs in the system. The paper
provides a rigorous analysis of situations in which
banks have incentives to bail out distressed banks.
Finally, an example of the benef its that can
emerge from interconnectedness can be found
in a recent paper by Gould et al.25 International
connections through trade, foreign direct
investment, migration, the internet and other
channels are critical for the transmission of
knowledge and growth as well as forming
macroeconomic linkages. But how much knowledge
is transmitted to a country is not only the result
of the overall level of connectivity, but also to
whom a country is connected, as well as how
these connections complement each other. For
example, being well-connected to an economy with
wide-reaching global connections is likely to be a
stronger conduit for knowledge transfers than being
connected to an isolated economy.
IS THERE AN OPTIMAL LEVEL
OF CONNECTIVITY?
In general, research has focused on the relationship
between the level of connectivity in a given network
and its resilience and function. Theoretical work has
focused on how the level, and type of connectivity
can result in increased resilience to the network.11,26
There is no economic theory at hand that can be
used to answer the question of the optimal level
of interconnectedness for a financial system from
a general equilibrium perspective; however, there
are attempts that try to answer this question from a
partial perspective.
The Bank for International Settlements (BIS)
has designed a regulation which aims to reduce
the maximum loss a bank could face in the case
of a failure of an individual counterparty. This is
one of the most relevant regulatory changes at the
international level (the other one is the mandatory
use of central counterparties for certain types
of derivatives), which has direct implications on
interconnectedness and the network structure in
the financial system. In particular, Batiz-Zuk et al.27
investigate the impact of establishing limits on
interbank exposures on the possible contagion in the
system. In this work, the authors simulate different
limits for interbank exposures and by resorting to
counterfactual simulations they compute the impact
of such different limits on contagion in the banking
system. One important conclusion from this work
is that by setting the interbank exposures limits
too low, contagion risk increases. This interesting
phenomena arises owing to the enormous increase
of connectivity in the banking system. This paper
illustrates very clearly that the apparent benefit of
higher connectivity does not always result in more
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risk sharing and could led to an increase in contagion
risk, despite the apparent robustness of the system.
Pichler et al.28 study the contribution to systemic
risk from common exposures, as defined by estimating
the degree of overlapping portfolios of different
counterparties. From there, the authors perform an
optimisation process that minimises systemic risk by
rearranging the network of common assets holdings.
This process performs such reconfiguration of the
individual portfolios preserving the same expected
return and risk. This work shows that despite the
difficulties involve on the optimal design of a network
structure, this is such a possibility, at least from a
central planer point of view. A similar approach can be
used to optimise, from the systemic risk perspective,
the structure for the exposures network.
On a theoretical level, some recent studies have
investigated the relationship between the level and type
of connections for a given network, and its resilience.
For example, Shai et al.29 have used the concept of
network modularity, or communities, to shed new
light on this issue. In real-world systems, the relatively
sparse interactions between modules are crucial to
the functionality of the system and are often the first
to fail. The authors model such failures focusing on
the interconnected nodes, those connecting between
modules, or communities, in the network. The authors
find — using percolation theory and simulations —
that a ‘tipping point’ emerges between two distinct
regimes. In one regime, removal of interconnected
nodes fragments the modules internally and causes the
system to collapse. In contrast, in the other regime,
while only attacking a small fraction of nodes, the
modules remain but become disconnected, breaking
the entire system. They show that networks with a
broader degree distribution might be highly vulnerable
to such attacks, since only few nodes are needed to
interconnect the modules, consequently putting the
entire system at high risk.
TOWARDS A MORE
COMPREHENSIVE DESCRIPTION OF
FINANCIAL INTERCONNECTEDNESS
As in many other complex systems, participants
in the financial system interact in many levels by
engaging in different types of financial transactions.
Complex systems can be adequately modelled
by multilayer networks. The field of multiplex
and multilayer networks already provides many
theoretical tools and applications in other domains,
such as transport infrastructures, social interactions,
ecological systems and brain functions.30 Likewise,
financial and economic connections are likely to
complement each other. For example, e-commerce
is often seen as a benefit of internet connectivity,
but without transport connectivity, e-commerce
may not amount to much. This novel framework
has recently been introduced for the modelling of
financial systems. In this section, we review some of
recent research on multilayer financial networks.
Overview of multilayer network research
in finance and economics
Bookstaber and Kenett31 proposed a multilayer
network to show how risks can emerge and spread
across the US financial system, which encompasses
both different types of financial institutions and
different types of financial activities. The three
layers in the map shown in Figure 1 represent
short-term funding, assets and collateral flows. The
layers are linked by large banks, hedge funds, central
counterparties (CCPs) and other market participants.
Risk is transformed and moves from one layer of
the network to the next through transactions among
large market players. The multilayer network reveals
potential channels of contagion that are not visible
in single-layer network. A risk to an activity in one
layer can become a risk to activities in other layers.
For example, a large bank or dealer facing a shortfall
in funding might reduce its lending to several hedge
funds (funding layer), and the hedge funds might
respond by liquidating assets (asset layer), resulting
in a drop in asset prices that affects collateral values
(collateral layer). The paper uses the difficulties
faced by Bear Stearns and its two failed hedge funds
during the financial crisis as a case study to illustrate
how the multilayer network can shed light on
potential vulnerabilities and paths of contagion. The
map requires detailed data to illustrate the full scope
of interconnections in the financial system.
Poledna et al.32 focused on bank interactions at
four layers (of financial contracts) such as interbank
credit, derivatives, foreign exchange and securities,
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Figure 1: The financial system participants and financial activities of funding, collateral and asset transactions are presented as a
three-dimensional multilayer network. Some financial entities, such as the bank/dealer, participate in more than one layer, thereby
connecting the layers. The multilayer approach establishes a framework for mapping the financial system across participant types and
activities, and modelling both the spread of shocks, as well as recovery, in one framework. See ref. 31 for source and further details
and quantify the daily contributions of these layers
to systemic risk in the Mexican banking system
from 2007 to 2013.32 They found that focusing only
on a single layer, as in a monoplex arrangement,
would underestimate systemic risk by 90 per cent.
Furthermore, they argue that market-based systemic
indicators such as VIX or CDS spreads also typically
underestimate expected losses from systemic events
since they are not capable of taking cascading defaults
into account. They also found that recently the
expected systemic losses are about four times higher
than they were before the global financial crisis of
2007. The authors point to the non-linearity of their
systemic measure, where in the systemic risk of the
combined exposure network is higher than the sum
of the systemic risk of the individual layers. They
argue that the main reason for this observed effect
is the propagation of shocks to financial institutions
between these layers. The authors develop a systemic
risk model based on a multiplex network for the
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Mexican banking system. In the paper, the authors
compute a measure of systemic risk which includes
four different layers of exposures. The authors also
demonstrate that by adding up the systemic risk
contribution of each independent layer, instead of
doing it for the multiplex, could lead to a serious
underestimation of systemic risk. In a related work,
the authors extend their approach33 and include the
layer of common assets holdings and compute an
indicator of systemic risk. Both works show that
considering only the individual layers independently
leads to an important underestimation of systemic
risk.
Using data on exposures between large European
banks that are broken down by maturity and
instrument type, Aldasoro and Alves17 characterised
the main features of the multiplex structure of the
network of such banks by defining two layers:
instrument and maturity. They found that well
connected banks in one network were also likely
to be well connected in the other networks. They
also found that both these layers exhibited a high
degree of similarity in both standard similarity
analyses as well as core-periphery analyses carried
out at the layer level. They represented a core-
periphery structure with a larger core in comparison
to studies using country-specific datasets. Their
main contribution is their development of two
measures of systemic importance that are well-
suited to cases where banks are connected through
an arbitrary number of different layers such as
instrument, maturity or a combination of both.
The most important limitation of their work is
that the two layers defined by the authors are not
derived from many different market activities;
however, this is common, given the extreme
difficulty of having access to data for many different
markets.
Focusing on countries from the Europe and
Central Asia region, Gould et al.25 proposed the
concept of multidimensional economic connectivity.
The authors show that multidimensional
connectivity is an economically and statistically
important determinant of future economic growth
for the set of investigated countries. The paper
further discusses the potential risks and transfer of
shocks that can result from cross-country economic
connectivity. Furthermore, it provides some
examples of how policy tools can be designed to
leverage the benefits of connectivity channels and
mitigate their risks.
Modelling the structure of multilayer
financial networks
An important concept in financial networks is
that of core-periphery, as was proposed by Craig
and von Peter.34 The idea behind this model is
that there are markets in which some institutions
are forced to limit the number of counterparties
they interact with. The reasons for this can be
multiple and depend on the kind of relationships
among the counterparties. When this happens,
a group of institutions intermediate between
other counterparties that cannot interact among
themselves. The group of institutions that act as
intermediaries are part of the core, while those
that do no interact among themselves belong to the
periphery. If the market has a perfect core-periphery
structure then each institutions from the core
will be connected with all others, and connected
with at least one counterparty from the periphery.
On the other hand, institution belonging to the
periphery will be completely disconnected among
themselves and they will interact with at least one
counterparty from the core. The probability of two
institutions being connected is near to one if both
counterparties are members of the core, near to 0
if both belong to the periphery and intermediate if
one comes from the periphery and the other from
the core. This definition can intuitively be extended
to the multiplex context by asking that the joint
probability of two banks of being connected is one
or 0 depending whether they belong to the core or
to the periphery.
The core-periphery model in ref.34 might be
quite suitable for unsecured interbank markets,
but this might not be the case for other market
activities as has been reported for the repo market in
Mexico.35 Moreover, there is no similar model to the
one proposed in ref.34 in a multiplex context. This
is why de la Concha et al.36 resorted to stochastic
block models (SBMs) in a multiplex context. A
core-periphery structure can be thought as a SBM
in a uniplex network where the number of blocks
is 2. SBMs were first introduced by Nowicki and
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Figure 2: (Continued)
Jan Feb Mar Apr May Jun JulAug SepOct NovDec
2007
Jan Feb Mar Apr May Jun JulAug SepOct NovDec
2008
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Jan Feb Mar Apr May Jun JulAug SepOct NovDec
2010
Jan Feb Mar Apr May Jun JulAug SepOct NovDec
2015
Figure 2: Evolution of clusters
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Snijders37 and are a useful tool to uncover the latent
structure in complex networks. The main hypothesis
is that the attributes of agents affect the way they
interact with each other. For example, it is expected
that a small bank will have less activity with other
institutions compared to a big bank. Agents with
similar attributes are classified into the same class and
the relation between agents is conditioned to
the cluster they belong.
In order to relax the definition of the core,
it is possible to redefine a core as a group of
counterparties that are interconnected with a
probability near to 1, whereas a periphery will
be a group of counterparties that interact with
each other with a low probability, near to 0.
Additionally, this def inition can be easily extended
to the multiplex case, where instead of analysing
the marginal probabilities of each market one can
use the joint probability distribution of the links in
the multiplex market. De la Concha et al.36 were
able to find the block structure across time for the
Mexican banking system. The authors analysed
the relationships among banks in seven different
layers without taking into account the strength of
these connections. A Bernoulli multilayer SBM
was enough to uncover the underlying structure
of the system. In order to have an idea of the time
component, the authors analysed the system in four
different periods: 2007, 2008, 2010 and 2015. In
Figure 2, it is possible to see that at the beginning
of 2007 the banking system was probably a core-
periphery network. From mid-2007, however, the
system is composed by a strongly connected core,
a less connected component and the periphery.
Additionally, during 2008, there were many
changes in the membership of the groups, this
could be associated with the GFC. During 2010 and
2015, there was little change in the structure of the
groups.
To conclude this section, as has been presented
here, interconnectedness and financial stability
are intrinsically related. Single layer networks
have been used in many previous contagion
studies to determine to interconnected to fail
institutions and for systemic risk modelling.
Nevertheless, this has been done without
considering the very important fact that financial
institutions interact in many different activities at
the same time and that in order to develop better
network models for financial stability, it is
necessary to resort to multilayer models, as was
illustrated by the many examples discussed in this
section.
NOVEL STATISTICAL METHODS
FOR MODELLING AND MEASURING
INTERCONNECTEDNESS IN
FINANCIAL SYSTEMS
One of the current frontiers in statistical models
for networks is being developed under the latent
space representation of networks. The seminal
work Hoff et al. proposed that ‘the probability of a
relation between actors depends on the positions of
individuals in an unobserved social space’,38 where
two agents are more prone to be connected if they
are closer in the latent space. Visualisation and
analysis of the space will therefore reveal important
aspects of the connectivity structure in the system.
The original model has been expanded in recent
years to encompass more complex characteristics of
networks. (See Kim et al.39 for a review of dynamic
latent network models.)
The complex characteristics of financial
networks — dynamic, multilayer, directed and
weighted — pose a challenge for the construction
of a unified comprehensive probabilistic model
that captures these characteristics. A recent model
proposed by Carmona and Martinez-Jaramillo,40
introduces a novel latent representation for networks,
which captures the intricate dependency structure
of a financial network. The model has been
successfully implemented in the Mexican banking
system.
Here, we illustrate the potential of these methods
by showing its application to one specific dataset.
The data under analysis consisted of financial
interaction between 44 banks during the years 2008
to 2011 for three different transactions (layers):
unsecured loan, repurchase agreements and trading
of financial assets.
The results of the inferential process provide
enlightening information about the underlying
connectivity of the banking system. For instance,
the estimated propensity of connection between all
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© Henry Stewart Publications 1752-8887 (2019) Vol. 12, 2 168–183 Journal of Risk Management in Financial Institutions 179
agents in the system for a given month is illustrated
in Figure 3. Each bank is represented by a circle
in this graph, whereas the distance between them
and the width of line linking them represents the
probability of being connected. There is a clear
structure captured by the model, which allows to
easily identify the centrality and relevance of each
actor in the system.
The dynamic of the interaction between banks
is also learned by the model. In Figure 4, the
evolution of the relation between two banks is
depicted. The left panel shows the probability of
connection between them as a function of time. We
see that there is a clear gradual increase in unsecured
transactions from bank (11) to bank (1) during 2019
(time 13 to 24).
The right panel shows the expected volume for the
transaction (conditional on its occurrence). The points
in both graphs correspond to the observed outcome
(0/1 for link existence in the left and a positive weight
for the transaction volume in the right).
It is worth saying that stress testing for the
quantification of systemic risk is a potential area
of future application and research for this class of
models. Current methods for systemic risk have
hitherto used truncated re-sampling of observed
networks, without acknowledging the underlying
probabilistic generative model. The novel inferential
framework offered by these models offers the
possibility to truly stress the joint connectivity
between agents, and consequently a more realistic
quantification of systemic risk.
Figure 3: Underlying interconnectedness in the unsecured market for a (randomly) selected day, estimated by the latent space model
fordynamic multilayer networks. Actors positions are obtained by applying the force–directed placement algorithm from ref.41. The
widthof the edges are proportional to the probability of connection between two agents on that day. The size of the nodes represent the
centrality of the node given by their aggregated strength
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Figure 4: For a — random — pair of banks (i = 11, j = 1), we show the dynamic of the strength of unsecured transactions from bank i to
bank j across time (monthly activity, time = 0 corresponds to January 2008). On the top panel, the posterior distribution for the probability
of connection, mean pˆ represented by the solid line, and the observed activity represented by the dots (0/1). On the bottom panel, the
expected amount for the transaction (conditional on being connected), and the actual amount also represented by the dots. All quantities
are estimated simultaneously within a comprehensive Bayesian model
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CONCLUSIONS
In this paper, we discuss different aspects of the
relationship between interconnectedness and
financial stability. As happens in many other
relationships, there are positive and negative
aspects. On the positive side, higher levels of
connectivity are associated with higher risk sharing
and higher resilience; on the negative side, higher
interconnectedness is associated with more systemic
risk owing to contagion and increasing complexity.
Moreover, financial contagion can take many forms
and all are associated with higher connectivity;
solvency contagion, funding liquidity contagion and
common assets holdings contagion.
Further work is still needed to understand
the relationship between the financial system’s
underlying structures affects financial stability;
nevertheless, without including it explicitly into
systemic risk models and stress testing, a serious
underestimation of systemic risk would be taking
place. Along this line, the new statistical models
and multilayer approach should be considered
as important tools for the second generation of
network models for financial stability monitoring
and analysis. Finally, in addition to an increase in
systemic risk associated with higher connectivity,
there is an important increase in the complexity
of the financial system. Such complexity is hard to
control for regulators and it is particularly important
when the financial authorities are in the middle
of a resolution process. Therefore, it is important
for researchers in financial networks and financial
stability to investigate and develop further their
tools and models as is being done in other scientific
disciplines.
Disclaimer
The opinions expressed in this paper are those of
the authors and do not represent the views of Banco
de Mexico or its board, or any other institution the
authors are affiliated with.
Acknowledgments
The authors are grateful to Alejandro de la Concha
for allowing us to use some of the results produced
by him from a previous project.
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