ActA všfs, 1/2014, vol. 864
Modelling Interconnections in the Global
Financial System in the Light of Systemic Risk
Modelování vazeb v globálním inančním systému
z pohledu systémového rizika
TOMáš KLINGER, PETR TEPLÝ
Abstract
in this paper, we focus on the link between systemic risk and sovereign crises. We model
how state support may inluence a distressed inancial system on an agent-based network
model calibrated to 4Q 2011 data collected from several sources. our model contributes
methodologically to agent-based modelling of banking networks’ systemic stability by
adding the sovereign sector and the mechanisms of risk transfer between the banks and
the sovereigns when state aid is initiated. the model implements two types of state support
to banks, bailouts and asset relief. We show that these two have diferent efect on
systemic stability, but both mitigate the systemic crisis in the short run. How the state aid
measures are eicient in the long run depends on the model’s parameterization.
Keywords
agent-based models, bailout, contagion, inancial crises, inancial stability, liquidity risk,
network models, systemic risk
JEL Codes
C63, d85, G01, G21, G28
Abstrakt
tento článek se zaměřuje na propojenost inančního systému s krizí státních inancí. Za
pomoci multiagentního síťového modelu zkoumáme, jak státní pomoc bankám ovlivňuje
inanční systém v krizi. Model je následně kalibrován na dataset za 4Q 2011, poskládaný
z různých zdrojů. Hlavním přínosem našeho modelu pro metodologii multiagentního
modelování inanční stability je přidání sektoru jednotlivých států a mechanizmu přenosu
rizika mezi bankami a státy v případě státní pomoci. Model implementuje dva základní
typy státní pomoci, rekapitalizaci a odkup aktiv. Ukazujeme, že tyto dva typy mají různý
efekt na stabilitu inančního systému, ale oba v krátkém období tlumí systémovou krizi.
Účinek těchto opatření v dlouhém období pak závisí na parametrizaci modelu.
ActA všfs, 1/2014, vol. 8 B65
Klíčová slova
multiagentní modely, státní pomoc, nákaza, inanční krize, inanční stabilita, likviditní
riziko, síťové modely, systémové riziko
Introduction
the recent global crisis started as a crisis of the credit system, continued as a crisis of liquidity
and with negative sentiment and overall market slowdown, it inally transformed
into economic crisis. in the earlier stages, the sovereigns took an active role, supporting
the economic system by bank aid, deposit guarantees, quantitative easing and economic
stimuli packages. However, large state support for the inancial system as well as for the
economy represents a huge burden on government inances and in some cases, mainly
in Europe, it has already resulted in sovereign debt crises. Moreover, losing their status
of risk-free borrowers and facing increasing prices for credit, the sovereigns too are now
signiicantly weakened and some are in threat of default. Since a large portion of sovereign
debt is held by the banking system, there is a danger of the crisis feeding back to
where it began in a vicious circle of transferring the toxic debt back and forth between
the sovereign and the inancial sector.
the overall aim of this paper is to contribute to the discussion on sovereign debt crises and
bank crises, which has been recently going on both on the EU and the international level.
the main research question is how the stability of the inancial system is afected by state
aid, how and when a systemic crisis can translate into sovereign crisis and how and when
a sovereign crisis can feed back into the system through sovereign debt exposures. the
main idea is that banks represented by their balance sheets form nodes in a inancial network.
Using a computational model, we simulate progression of shocks in the network
given various types and levels of state aid. our approach stems from the recent advances
in agent-based network modelling of inancial systems, mostly from Nier, et al. (2007).
the following second section will focus on the description of the link between the inancial
institutions and the sovereigns, mostly in regard to the recent inancial crisis. the third
section will present the used concepts, presenting a literature review of the modelling
techniques that form the grounds for our analysis. in the fourth section, we construct an
original model of a inancial system which will be used for testing the impact of the sovereign
assistance to banks and researching the feedback loops that may arise when such
assistance weakens the sovereigns. in the sixth section, we calibrate it to a unique dataset
collected from various sources in order to gain more insight into the current situation and
outline some practical implications for setting new policies in case of a systemic banking
crisis. Finally, we close the paper with a conclusion summarizing our research and indings.
1 The Current Financial Crisis
the true mark of the systemic crisis outbreak was the failure of lehman Brothers on 15
September, 2008. Even though its bankruptcy meant a very signiicant shock to the interbank
system, the other reason for the crisis to inally break out was psychological. Understanding
that state aid is no longer guaranteed even for large, systemically important
banks, the share prices of the banking sector plummeted as the investors were no longer
ActA všfs, 1/2014, vol. 866
willing to consider inancial institutions as an investment opportunity. Moreover, the market
of bank debt funding froze and liquidity evaporated from the interbank market. the
banking system thus found itself in a deadlock where it was not able to roll over the shortterm
debt it used to inance most of its operations, but at the same time, the individual
institutions held unsettled overdue claims against each other. Moreover, due to the increased
cost of lending and severe credit shocks, the banks’capital bufers did not suice
to prevent the system from collapse. Had they not been replenished, a large portion of
the banking system would have failed.
Figure 1: Financial sector support in selected advanced economies, 2008 – Jul 2012
Panel A: total direct support Panel B: Unrecovered support – impact on
public debt
Source: IMF (2013a)
At this point, the states started playing an active role, introducing a number of measures
to support the troubled inancial institutions. Amongst these measures were strengthening
of the deposit insurance, state guarantee schemes, outright bail-outs for bank recapitalisation
or loans to alleviate the severe lack of liquidity (liikanen, 2012). Mostly in
Europe, several states introduced bad loan buy-outs or complete bank nationalizations
(Petrovic & tutsch, 2009).
Figure 1 shows the inancial sector support in advanced countries as a fraction of the
2012 GdP along with its recovery values. the top rank in terms of GdP fraction belongs to
ireland followed by Greece. in March 2013, Cyprus bailed out its banks using the EUr 10
billion in funds provided by the European Central Bank and international Monetary Fund
as the ifth European country to receive such assistance (ECB, 2013). in the short run, the
support measures had a positive impact on systemic stability. Panetta, et al. (2009) states
that the government support managed to lower the banks’ credit default swap (CdS)
premiums, which is the main indicator of failure risk. the irst drop came when a support
measure was announced and subsequently, the premiums fell even further when each of
the measures was implemented. Moreover, the larger the amount of funds employed in
a support measure, the sharper was the decrease of CdS premiums. Finally, there were
ActA všfs, 1/2014, vol. 8 B67
positive spill-over efects of these measures illustrated by falls of CdS premiums in countries
other than the one deploying the measure.
However, the above-mentioned support actions proved to be very expensive and progressively,
the situation started deteriorating for the sovereigns. As the balance sheet
weaknesses moved from the banks to the sovereigns and the tax revenues dropped, the
iscal deicits began to surface. As the individual countries’ creditworthiness crumbled
and the rating agencies pointed out the associated risks, the investors began panicking
and losing conidence even in the sovereign states. As a result, sovereign bond yields and
CdS spreads rose and the access to new funding became increasingly more expensive. in
a situation like this, when a sovereign guarantee is exercised or a large bank needs to be
fully or partially bailed out and on top of that a country inds itself in an economic downturn,
the public accounts are in serious trouble.
Unfortunately, the sovereigns did not prove to be anything else than other type of agents
in the same inancial system and thus by taking the risk on themselves, it did not vanish.
instead, it returned in form of feedback loops from the sovereigns back to the banks later
when the sovereigns found themselves in crisis and their own balance sheets were deteriorating.
in this manner, the risk and the losses oscillated between the privately-held
banks and “publicly-held” sovereigns.
2 Modelling Approach
the modelling framework is based on two central concepts, network theory and agentbased
modelling. Network theory is particularly useful for description of connected structures
and the pattern of their relationships. A network is a set of nodes connected with
edges.10
Nodes may represent individual agents, for example servers and websites when
we study computer networks or people in case of social networks. in the framework of
inance, they may represent banks, sovereigns, depositors, companies or other entities in
a inancial system. Edges contain data on connection of any two particular nodes in the
network, determining whether there is a link between two nodes and what is its value
and direction. When the network theory is applied to modelling of inancial systems, such
properties allow us to deine the creditor/debtor relationships as well as the size of the
mutual claims of individual banks (Klinger, 2011). Network theory proved to be a particularly
interesting means of studying impulse transmissions, which includes transmission of
negative shocks. We use this methodology for simulating credit shocks in banking systems
since when one bank fails and there are no supporting mechanisms such as bail-outs or
state guarantees, the losses are transmitted to its creditor banks.
Agent-based modelling is a bottom-up approach that examines how numerous subjects
that are each equipped with basic set of data and behavioural rules are interacting in
a virtual environment. According to tesfatsion (2006, p. 835),“[an agent] refers broadly to
bundled data and behavioural methods representing an entity constituting part of a computationally
constructed world“. the individual agent’s actions inally lead to certain ag-
10 More rigorously, network is a graph defined as , where is a set of nodes, is a set of edges and is the mapping
function which plots the edges onto individual pairs of nodes (Lewis, 2009).
ActA všfs, 1/2014, vol. 868
gregate behavioural patterns on the systemic level. Probably the most well-known paper
describing macro-level efects stemming from micro-level behaviour is the one by Schelling
(1969), who described how a simple set of individuals’ preference of the composition
of their neighbourhood may lead to a pattern of segregation on a systemic scale. in our
model, the agents represent individual inancial institutions or sovereigns, the basic data
they hold are their balance sheets and a set of behavioural rules such as when to default,
when to sell of a particular amount of assets or when to bail out a certain institution.
Current research applying the previously mentioned methods to the ield of inancial or
banking system stability divides into two main streams: empirical research and theoretical
models. Several studies concentrate on the real-world interbank exposure modelling. For
example Boss, et al. (2004), Upper & Worms (2004), Wells (2004), Van lelyveld & liedorp
(2006) or Muller (2006) analyse the banking systems of Austria, Germany, the United Kingdom,
the Netherlands and Switzerland respectively. recently, Halaj and Sorensen (2013)
tried to approximate a network of the banks who reported during the 2010 and 2011 EBA
stress tests. However, most of the researchers face the problem of virtually non-existent
reliable data on individual interbank exposures.
theoretical models examine how system behaviour is inluenced by its general characteristics.
the irst such model was constructed by Allen & Gale (2000) who studied contagion
of funding liquidity shocks. Another early analysis was carried out by Freixas, et al.
(2000), who studied contagion in systems where some banks were systemically important.
Cifuentes, et al. (2005) and Shin (2008), add a market liquidity contagion channel decreasing
the price of illiquid assets. Finally, there are studies that analyse systemic stability by
simulation experiments on random networks such as Gai & Kapadia (2010), or Nier, et al.
(2007). Finally, Klinger & teply (2014) add regulatory aspects into this framework. this
paper combines theory and empirics as the model is calibrated to the real-world data.
3 The Model
For each individual simulation, our model is deined in several steps. First, the network
of banks and sovereigns is initialized together with the balance sheet data of individual
agents. Second, the system is stressed by a credit shock, which may originate from a particular
bank in the network. Following the initial shock, the stress propagates through
the network and may trigger actions of the particular agents such as bank or sovereign
defaults, asset ire-sales or state assistance to troubled banks. the simulation continues
in several laps until the initial shocks completely dissolve and are no more transmitted
further onto other agents.
First, the network is built from the calibration dataset. the total value of all assets in the
system upon initialization is a sum of:
a) interbank assets, constituted by all the loans represented by the edges of the interbank
network,
b) sovereign debt, constituted by individual banks’exposures towards their domestic sov-
ereigns,
c) external assets, constituted by individual banks’ exposures outside the network, e.g.
loans to other entities (e.g. households, businesses or foreign sovereigns) or derivatives.
ActA všfs, 1/2014, vol. 8 B69
the inal setting of banks’ balance sheets is depicted in table 1.
Table 1: Balance sheet variables of a modelled bank
...TOTAL ASSETS ...TOTAL LIABILITIES
...sovereign debt ...interbank liabilities
...interbank assets ...external liabilities (deposits)
...external assets ...equity (capital bufer)
Source: Authors
When the network is prepared, the system is inactive until we impose a shock event initiating
the irst simulation lap. Similarly, at the beginning of each next lap, each bank may
receive a total asset-side shock of , where
• represents losses that banks incur due to default of another bank in the network to
which they hold an exposure.
• represents losses that banks incur due to overall drop in asset prices caused by market
liquidity efects.
• represents losses that banks incur due to default of a sovereign in the network to
which they hold an exposure.
these individual components are described in detail on the following pages.
4 Shock Reaction and Contagion
if the banks afected by the primary shock do not have suicient capital bufers, a process
of cascade contagion efects may unfold, where in each lap of the simulation, the banks
that default transmit the shock further onto other banks in the system. Figure 2 depicts
the mechanism of shock propagation; the shock-transmitting banks are coloured grey
whereas the failed banks are depicted in black.
Figure 2: Scheme of banking system contagion
Source: Klinger (2011) inspired by Sell (2001)
let us consider a bank that receives a shock. Whatever the shock type, it is relected in the
balance sheet and the bank loses a certain part of its assets. Since the sum of assets must
If the banks affected by the primary shock do not have sufficient capital buffers, a process of
cascade contagion effects may unfold, where in each lap of the simulation, the banks that default
transmit the shock further onto other banks in the system. Figure 2 depicts the mechanism of
shock propagation; the shock-transmitting banks are coloured grey whereas the failed banks are
depicted in black.
Figure 2: Scheme of banking system contagion
Source:
Let us consider a bank that receives a shock. Whatever the shock type, it is reflected in the
balance sheet and the bank loses a certain part of its assets. Since the sum of assets must equal
the sum of liabilities, the bank has to write off an equal value of liabilities. Firstly, the shocks
are absorbed by owners’ equity but if the capital buffers are not large enough, the banks default
on claims of other creditors. If in lap  the -th bank suffers an initial shock, its external
ActA všfs, 1/2014, vol. 870
equal the sum of liabilities, the bank has to write of an equal value of liabilities. Firstly,
the shocks are absorbed by owners’equity but if the capital bufers are not large enough,
the banks default on claims of other creditors. if in lap the -th bank sufers an initial shock,
its external behaviour depends on the shock size relative to its balance sheet structure:
a) At irst, the shock hits the bank’s capital bufer. if the shock is smaller than the bank’s capital
reserve which means that the bank is able to cover the losses by its own equity, then
the capital bufer absorbs the shock completely and the bank does not send it further
to other agents in the system.
b) if the capital reserve is not large enough, the residual shock overlows to the interbank
liabilities, in which case its value up to the value of the interbank liabilities is uniformly
divided into losses of all creditor banks which receive a CreditShock proportional to the
size of their exposure to the failing bank. As the failing bank defaults, in the next lap it
is removed from the system. Also, in the next lap of the simulation the creditor banks
evaluate the received shock. the simulation inishes when there is a lap when no bank
propagates the shock further.
c) Additionally, it holds that:
i. if the shock is smaller than the sum of the bank’s capital reserve and its interbank
liabilities, it is absorbed completely by these two balance sheet items
ii. if the shock is larger than the sum of the bank’s capital reserve and its interbank
liabilities, the shock overlows to external liabilities, meaning that the
residual loss is covered by the depositors.
4.1 Market Liquidity Risk Modelling
Market illiquidity, described irstly by Kyle (1985), represents a situation when transactions
in which the assets are sold have a negative impact on the asset prices.11
Along with Gai &
Kapadia (2010), we assume that in case a bank is in default, it has to liquidate all of its assets
before it is removed from the system. While the sovereign debt is assumed to be more
liquid and hence is liquidated in full value, the low market depth may limit the capacity
to absorb the external and interbank assets. As a result, these cannot be sold for the price
for which they are kept in the bank’s books. Following Cifuentes, et al. (2005), we assume
an inverse demand function for the external assets, which takes the form of
() = exp −


 ,


,

,
 
()

 = ,().
Where is the number of banks in the system, is the total value of assets (external and
interbank) sold by the -th bank in the system in the current lap, represents the market illiquidity
(i.e. the speed at which the asset price declines) and is the new discounted price
11 Market liquidity is usually measured by indicators such as market depth, resiliency, tightness, and volatility.
These indicators may be aggregated into liquidity indices, which then can be used to quickly compare markets
in time and cross-sectionally. Examples of market liquidity indices are found e.g. in Gersl & Komarkova,
(2009) or Teply, et al. (2012).
ActA všfs, 1/2014, vol. 8 B71
of external assets calculated in each lap.12
the additional losses caused by the asset sales
are then added to the initial shock on -th bank in the current lap and transmitted accordingly.
Furthermore, assuming marking to market accounting, at the end of each lap the
external assets of each bank are revalued such that
() = exp −


 ,


,

,
 
()

 = ,().
ℎ, = ,(() − ())
a. Bailouts	and	recapitalization	
 Δ, 
Δ,

= 
Δ,

b. Asset	relief
฀฀,฀
(1 − 
), 
,
1 − 
() = 1.
Hence, the losses stemming from such price adjustment result in a price shock of to all
banks.
4.2 The Role of Sovereigns
As a means of a sovereign to support its domestic banks, we introduce two possibilities of
sovereign assistance. these include:
a) Bailouts and recapitalization (Br) – the sovereigns may pay for losses incurred by the
banks to replenish their capital bufers and keep them in business. in this case when
a bank receives a shock of , the sovereign covers , adding this value to the bank’s external
assets. Again, the amount of is then added to the external debt of the -th banks’
domestic sovereign as the domestic government needs to ind external inancing for
this rescue measure.
b) Asset relief (Ar) – the sovereigns may buy what assets their domestic banks need to sell
in ire sales. in this case, in each round every bank sells assets as described in the basic
model deinition, but only is sold on the market since is bought-out by the bank’s domestic
government. Assuming ixed across all banks and all sovereigns, Equation 1 is
replaced by:
() = exp −(1 − )  ,


,

= 
, the amount of is then added to the external debt of the -th banks’domestic sovereign as
the domestic government needs to ind external inancing for this rescue measure.
As we mentioned previously, sovereign assistance may work very well for short-term
banking system stabilization, but it puts signiicant pressure on the intervening sovereigns.
According to Acharya, et al. (2012), state assistance to banks requires that the sovereigns
immediately issue new debt to inance such measures, which results in immediate
increase in the sovereigns’ credit risk through the liability side of their balance sheets. in
the model, any type of sovereign assistance to the banks results in an increase of the debt
of the domestic sovereign. the extra budget deicit resulting from the aid measures is the
main driver of a credit risk increase in the model.
the sovereign credit risk in the model is represented by probability of default, which under
a certain assumed recovery rate may be roughly approximated from the CdS spreads.
12 Upon the system’s initialization, the price is set to
ActA všfs, 1/2014, vol. 872
Credit default swaps are contracts insuring against credit events on bonds in case the
counterparty defaults. the buyer pays periodically to the seller until either the CdS matures
or until a credit event occurs, in which case the buyer of the insurance is entitled to
sell to the seller of the insurance the insured bonds for their face value (Hull, 2008). As our
model is of short-term character and later on, we calibrate it to yearly data, we chose to
implement the probability that a given sovereign defaults in one year. Although strictly
speaking, the extraction of this probability from the available 5-year CdS spreads would
require diligent modelling of both the default state and the no-default state cash lows,
we can simplify the calculation by assuming a lat CdS spread curve and implement the
widely used approximation according to J.P. Morgan and Company & riskMetrics Group
(1999):


= 
, 
,

=  1 −
1
1 +
,
1 − 
,
,

,
τ
τ = = .

, = , + 
,

.
 ,

ℎ
Where is the probability that a given sovereign defaults in one year, is the annual CdS
spread, is the recovery rate and is the number of years for the cumulative default probability
calculation (in our case, and in line with common practice, ).
the link between sovereign deicits and credit risk is documented by econometric studies
such as Attinasi, et al. (2009) or Cottarelli & Jaramillo (2012). We use the following equation
to update the sovereign CdS spreads at the end of each simulation lap (parameter is later
on referred to as the CdS sensitivity):

= 
, 
,

=  1 −
1
1 +
,
1 − 
,
,

,
τ
τ = = .

, = , + 
,

.
 ,

ℎ
Putting the previous points together, at the end of each lap the model collects the total
amount of each sovereign’s deicit and feeds it into Equation 3 which is then plugged
into Equation 4. At the beginning of each simulation lap, a sovereign may default with
probability . in that case, each creditor bank receives a  equal to the size of exposure to
the defaulting sovereign multiplied by . the sovereign debt on its balance sheet is then
revalued accordingly.
5 Empirical Analysis
in the following chapter, we calibrate our model to the real-world banking data in order
to contribute to the current debate on systemic stability and the link between banks and
sovereigns. As documented by many authors (e.g. Mistrulli, (2011)), the data on individual
banks’mutual exposures is not available. therefore, we resort to proxy data inferred from
available sources to build the interbank network. instead of individual banks, the agents
in our study represent banking systems of countries which report their banking positions
to BiS (referred to as subsystems since they are all part of the global banking system) and
these agents’balance sheets are composed of aggregated igures of all banks reporting in
ActA všfs, 1/2014, vol. 8 B73
their domestic countries. the“interbank”exposure data are complemented with banking
system data collected from several sources to provide a complete picture of the global
banking system.
5.1 Data Deinition
to calibrate the model to the real-world igures, we collected data from several sources.
table 2 shows the main items which we describe further in greater detail.
Table 2: Banking system balance sheet with data sources
TOTAL ASSETS (EBF Database, Central banks)
Government debt (Arslanalp &Tsuda (2012), IMF IFS Database) External liabilities (Calculated)
Interbank assets (BIS International Statistics) Interbank liabilities (BIS International Statistics)
External assets (Calculated) Equity (BankScope)
+GDP (World Bank), CDS Spreads for the individual countries (Bloomberg)
Source: Authors
5.1.1 Interbank Assets and Liabilities
the interbank exposure dataset describes the interlinkages in the global banking system.
these are collected from the banking section of BiS international Financial Statistics (BCBS,
2013), where the central banks report compiled national aggregates calculated from data
on individual banks’ in their jurisdiction. to form the interbank exposure matrix, we employ
data from the consolidated statistics of foreign claims on immediate borrower basis.
the consolidated data provides information on exposures of domestically-owned parent
banks on the highest consolidation level and hence they include external exposures
of own foreign oices and exclude all internal inter-oice positions in the consolidation
group (BCBS, 2009). the selection of countries whose banking sectors we included in the
analysis was based on data availability and includes Australia, Austria, Belgium, Brazil,
Canada, denmark, France, Germany, Greece, ireland, italy, Japan, Netherlands, Portugal,
Spain, Sweden, Switzerland, turkey, the United Kingdom, and the United States.13
Nevertheless, it is not possible to obtain directly the pure bank-to-bank exposures between
the individual countries’banking sectors, and some level of approximation is inevitable.
to estimate the bank-to-bank exposures from the reporting banking sectors’ pool
of total claims, we employ another dataset of the BiS statistics, which is the total claims
on each country’s banking sector by all the reporting sectors, grouped by the type of the
debtor institution (i.e. whether it is a bank, public sector or a non-bank private sector). By
taking a fraction of bank debt on the total debt, we obtain proxy variables for individual
counterparties. Finally, we multiply the whole column of the exposure matrix representing
the given counterparty’s debts by this variable to calculate the estimated interbank
network.
13 Czech Republic was not included in the analysis as it does not report its international banking exposures to
BIS.
ActA všfs, 1/2014, vol. 874
When the network is created, it can be plotted as in Figure 3. For better readability, we
provide two diferent views for the same dataset. in Panel A, we show the edges of the
network (interbank exposures) coloured according to the source of the funds (i.e. the
creditor, the bearer of the risk). these visualizations provide an eicient overview of the
situation and a quick grasp of the basic relationships. For example, in the centre of the
network, we see the“core”sectors, (highly interlinked nodes such as the United States, the
United Kingdom, Japan, France, Germany or Switzerland) and around them there are more
“peripheral”banking systems. Also, as the visualization algorithm14
takes into account the
relationships in the network and places the nodes accordingly, we can see patterns that
are in line with our anticipation based on the individual countries’ location or cultural
relationships. Note for example the pairs of countries being placed together, such as Sweden
and denmark or turkey and Greece. Also, the clusters of related countries are placed
logically together, such as italy, Spain and Portugal forming the Southern Europe cluster
with proximity to Brazil. Also note that after its default, Greece is placed on the edge of
the network with very low connection to other banking systems.
14 The visualizations were prepared in Gephi software. For the calculation of the node layout, we used the
Force Atlas algorithm, which places the nodes in the graph according to the values of edges in the network
matrix. While the scientific article on Force Atlas algorithm is still awaiting acceptance and publication,
more information on graph clustering and layouting may be found in Noack (2007).
ActA všfs, 1/2014, vol. 8 B75
Figure 3: interbank network of the selected countries as of Q4 2011
Figure 3: Interbank network of the selected countries as of Q4 2011
Source:
Note:
It is necessary to mention that this dataset provides information only on interbank lending and
not on external financing of banks by sovereigns or central banks, which may be quite
Panel A:
Panel B:
Source: Authors based on data from BIS International Financial Statistics
Note: Panel A shows the edges shaded by the creditor node (e.g. exposure of Switzerland
against the United States has the same shade as Switzerland on the chart) whereas in Panel
B, they are shaded according to the debtor node (e.g. exposure of Germany against the United
Kingdom has the same shade as the UK node)
ActA všfs, 1/2014, vol. 876
it is necessary to mention that this dataset provides information only on interbank lending
and not on external inancing of banks by sovereigns or central banks, which may
be quite signiicant, especially in the Eurosystem. on the same note, these data do not
provide information on balances in the tArGEt2 system, which has been lately discussed
in Cecchetti, et al. (2012) and which now form a signiicant part in the mutual exposures
of the Eurosystem banks. the above-mentioned facts mean that Figure 3 does not provide
the entirely complete picture of the global banking system. However, in our model, bank
inancing of these diferent types is captured in the external assets part of the bank’s balance
sheet.
5.1.2 Sovereign Debt to Banks
to introduce the link between banks and sovereigns into the banks’ balance sheets, we
collected two sovereign debt datasets which were then added together. these are exposures
to the domestic banking system, collected mainly from Arslanalp & tsuda (2012)
and supplemented by data from the iMF iFS database (iMF, 2012), and exposures to other
banking systems, collected from the BiS international Financial Statistics (BCBS, 2013).
While the irst dataset collection is straightforward, in case of the second one we have to
employ a similar calculation as in the case of interbank assets. Again, the data is taken from
the consolidated statistics of foreign claims on immediate borrower basis. to estimate the
banks’exposures to sovereigns from the reporting banking sectors’pool of total claims, we
multiply the whole column of the exposure matrix representing the given state’s debts by
the fraction of its sovereign debt on the total debt. the same approach was used in Arslanalp
& tsuda (2012) for the calculation of foreign banking sector holdings of sovereign
debt. However, we must note that this data provide information only on the individual
sovereigns’debt towards the banking sectors in our sample. thus it does not describe the
countries’ total debt positions.
Figure 4 visualizes the igures for each sovereign’s debt to the foreign as well as to the domestic
banks. We see that for all banking systems except of the United Kingdom and the
Netherlands, there is a relatively strong bias towards the domestic banks (note the logarithmic
scale of the chart). this phenomenon already documented in Pisani-Ferry (2012),
Merler & Pisani-Ferry (2012) or Acharya, et al. (2012), results in a strong link between sovereigns
and their domestic banks through balance sheet exposures and is one of the reasons
why sovereign risk translates through feedback loops into the domestic banks’ risk.
ActA všfs, 1/2014, vol. 8 B77
Figure 4: Selected banking systems’ exposures to sovereign debt as of Q4 2011
Source: Authors’ calculations based on data from Arslanalp & Tsuda (2012), IMF International
Financial Statistics and BIS International Financial Statistics
For better insight into the interlinkages between banks and sovereigns, one has to study
also the individual exposures. Figure 5 presents this data as a plot of the bipartite network
of sovereigns and banking systems in our sample. Similar to Figure 3, the edges represent
the sovereign debt towards the individual banking system. Here we see the home bias
phenomenon as the largest links are always to the domestic banking system. Also for the
individual countries, interesting patterns emerge where the debt to foreign banks is determined
largely by geographical or cultural proximity of the individual countries.
Figure 5: detailed banking systems’ exposures to sovereign debt as of Q4 2011
towards the individual banking system. Here we see the home bias phenomenon as the largest
links are always to the domestic banking system. Also for the individual countries, interesting
patterns emerge where the debt to foreign banks is determined largely by geographical or
cultural proximity of the individual countries.
Figure 5: Detailed banking systems’ exposures to sovereign debt as of Q4 2011
Source:
Note:
Source: Authors’ calculations based on data from Arslanalp & Tsuda (2012), IMF International
Financial Statistics and BIS International Financial Statistics
ActA všfs, 1/2014, vol. 878
Note: The edges are shaded by the debtor node. The edges’ thickness represents the exposure
size on a natural log scale and all exposures amounting to less than USD 5 billion were filtered
out for better readability.
5.1.3 Other Data
the banking systems’ total assets represent another important input into the model as it
is used for calculation of capital, external assets and external liabilities of the individual
banking sectors. despite it being an important variable for comparison of banking systems
in time as well as in cross-section, the data on sums of total assets is not readily
available and vary signiicantly across data sources.15
to keep our dataset as consistent as
possible, the main source we used is the Banking Sector Statistics database of the European
Banking Federation (EBF, 2013), which provides data on all European countries in the
sample. the data on countries not represented in this primary source were taken from the
databases of the individual central banks.
the size of the capital bufers is the main determinant of the stability of the individual
banks as well as the whole system. in contrast to the total assets data, in case of banking
sector capitalization, we are interested in the proportion of capital to total assets rather
than the total sum and hence, the capital ratios were taken from the BankScope data-
base.
Besides balance sheet data for the individual countries’ banking systems, the model requires
two more datasets for a complete calibration: GdP and CdS spreads of the individual
sovereigns. the gross domestic product data was collected from the World Bank
database (World Bank, 2013), data on 5-year credit default swap spreads were obtained
from Bloomberg.
5.2 Model Calibration
Put all together, the collected data provide a complex picture of the modelled global
banking system according to table 2. the internal assets of individual subsystems are
calculated as the sum of their exposures to other subsystems; the sovereign assets as the
sum of their exposures to sovereigns and the external assets as the total assets minus the
internal and the sovereign assets. Similarly, capital is calculated as the collected capital
ratios times the total assets of the individual subsystems; their internal liabilities are sums
of their debt towards other subsystems, and the external liabilities are total assets minus
capital and the internal liabilities.
Figure 6 provides the inal overview of the calibrated balance sheets which are loaded
into the model. As we can see on Figure 6A, the external assets constitute the majority
of the bank’s balance sheets, in fact around 80%, while the sovereign assets account for
12% and the interbank assets only for 8%. Similarly on the liability side depicted in Figure
15 E.g. taking the same data from BankScope, the differences in some cases were significant. We explain this
by the fact that BankScope is not the best source for total sums of variables for individual banking sectors
(Bhattacharya 2003), and resort to the aggregated data from EBF and the central banks.
ActA všfs, 1/2014, vol. 8 B79
6B, external liabilities form an overwhelming 86% of the total liabilities while the banks’
equity accounts for 6% and the interbank liabilities for 8%. the fact that the interbank network
forms only a small portion of the total banking assets value is the main shortcoming
of the pure credit contagion approach. it points at the fact that without oversimpliied
extrapolation of the interbank network to the rest of the banking system, it is diicult to
draw any conclusions from works such as Chan-lau (2010) that study only the efects of
the direct contagion and funding shocks and relies solely on the BiS interbank network
data. in fact, our inding stresses the signiicant gap in the knowledge of banking exposures
and demands further data collection which would enable us to break the external
assets into more detail.
Figure 6: Balance sheets of the calibrated model as of Q4 2011
Panel A: Banks’ assets Panel B: Banks’ liabilities
;
;
Source:
;
;
Source:
Source: Authors’ calculations
As opposed to Chan-lau (2010), we incorporate the full size of the banking system and
the indirect channel of contagion through market liquidity as described by Brunnermeier,
et al. (2009) and Cifuentes, et al. (2005). Given the amount of external assets, we expect
that the liquidity channel will play a signiicant role for systemic stability. this channel is
recognized also by authors focusing on the direct credit contagion, as documented by
Upper (2011).
5.3 Efects of Sovereign Assistance
in this section, we will explore the efects of sovereign assistance on the calibrated global
banking system. We will describe the impact and costs of the two support measures.
Please note that in this phase the mechanism of risk transmission from the sovereigns
back to the inancial system (feedback loops) is not yet implemented.
ActA všfs, 1/2014, vol. 880
Figure 7: Bailouts and recapitalization efects
Panel A: total defaults
- Alpha vs. Bailouts ratio
Panel B: total cost
– Alpha vs. Bailouts ratio
As opposed to Chan-Lau (2010), we incorporate the full size of the banking system and the
indirect channel of contagion through market liquidity as described by Brunnermeier, et al.
(2009) and Cifuentes, et al. (2005). Given the amount of external assets, we expect that the
liquidity channel will play a significant role for systemic stability. This channel is recognized
also by authors focusing on the direct credit contagion, as documented by Upper (2011).
In this section, we will explore the effects of sovereign assistance on the calibrated global
banking system. We will describe the impact and costs of the two support measures. Please note
that in this phase the mechanism of risk transmission from the sovereigns back to the financial
system (feedback loops) is not yet implemented.
Figure 7: Bailouts and recapitalization effects
Source:
We first look at the bailouts support measure. Figure 7A depicts the number of bankrupt
banking subsystems given various levels of market illiquidity (฀, referred to as alpha) and
various intensities of state support (฀฀฀
, referred to as bailouts ratio). The positive effects of
this measure are clearly visible and with maximum bailout support, no bank defaults as the
shock is captured right at its origin. We see that at low values of alpha, the effect of state aid is
very low and almost linear. However, with growing illiquidity, the state support is increasingly
important and at maximum alpha, we see a “step-like” dependence where a very small increase
in state support may prevent default of three banking subsystems. As to the sovereign deficits
caused by this measure, Figure 7B demonstrates that at very low levels of alpha, the costs
increase almost linearly with the support intensity. However, for low capitalized systems, under
high levels of alpha, the costs rise only until some level of support intensity beyond which they
fall sharply. This is caused by the support measure effectively blocking the contagion through
market liquidity channel and corresponds to the sharp drop of defaults in Figure 7A.
As opposed to Chan-Lau (2010), we incorporate the full size of the banking system and the
indirect channel of contagion through market liquidity as described by Brunnermeier, et al.
(2009) and Cifuentes, et al. (2005). Given the amount of external assets, we expect that the
liquidity channel will play a significant role for systemic stability. This channel is recognized
also by authors focusing on the direct credit contagion, as documented by Upper (2011).
In this section, we will explore the effects of sovereign assistance on the calibrated global
banking system. We will describe the impact and costs of the two support measures. Please note
that in this phase the mechanism of risk transmission from the sovereigns back to the financial
system (feedback loops) is not yet implemented.
Figure 7: Bailouts and recapitalization effects
Source:
We first look at the bailouts support measure. Figure 7A depicts the number of bankrupt
banking subsystems given various levels of market illiquidity (฀, referred to as alpha) and
various intensities of state support (฀฀฀
, referred to as bailouts ratio). The positive effects of
this measure are clearly visible and with maximum bailout support, no bank defaults as the
shock is captured right at its origin. We see that at low values of alpha, the effect of state aid is
very low and almost linear. However, with growing illiquidity, the state support is increasingly
important and at maximum alpha, we see a “step-like” dependence where a very small increase
in state support may prevent default of three banking subsystems. As to the sovereign deficits
caused by this measure, Figure 7B demonstrates that at very low levels of alpha, the costs
increase almost linearly with the support intensity. However, for low capitalized systems, under
high levels of alpha, the costs rise only until some level of support intensity beyond which they
fall sharply. This is caused by the support measure effectively blocking the contagion through
market liquidity channel and corresponds to the sharp drop of defaults in Figure 7A.
Source: Authors
We irst look at the bailouts support measure. Figure 7A depicts the number of bankrupt
banking subsystems given various levels of market illiquidity (, referred to as alpha) and
various intensities of state support (, referred to as bailouts ratio). the positive efects of
this measure are clearly visible and with maximum bailout support, no bank defaults as
the shock is captured right at its origin. We see that at low values of alpha, the efect of
state aid is very low and almost linear. However, with growing illiquidity, the state support
is increasingly important and at maximum alpha, we see a “step-like” dependence where
a very small increase in state support may prevent default of three banking subsystems. As
to the sovereign deicits caused by this measure, Figure 7B demonstrates that at very low
levels of alpha, the costs increase almost linearly with the support intensity. However, for
low capitalized systems, under high levels of alpha, the costs rise only until some level of
support intensity beyond which they fall sharply. this is caused by the support measure
efectively blocking the contagion through market liquidity channel and corresponds to
the sharp drop of defaults in Figure 7A.
ActA všfs, 1/2014, vol. 8 B81
Figure 8: Asset relief efects
Panel A: total defaults
- Alpha vs. Bailouts ratio
Panel B: total cost
- Alpha vs. Bailouts ratio
Figure 8: Asset relief effects
Source:
Secondly, looking at the effects of asset relief programmes as depicted in Figure 8A, we see
that they do not cause such sharp drops in numbers of failed banks as those of outright bailouts,
but still are very significant. Because asset relief is tied to the liquidity channel, we see that the
shape of the dependence of systemic stability on the support intensity (฀฀฀
) is similar to the
shape of its dependence on (1 − ฀).Also, in contrast to outright bailouts which may be targeted
to the initial propagator, in case of asset relief, the banks which are hit by the primary shock
always fail. Looking at the costs of this measure, Figure 8B shows that at the peak they are
higher than those of the bailouts. Also, except for the area of support intensity of 0.8 to 0.9
where they are smoother, they have very similar shape as the costs of bailouts. The reason for
asset relief to prove such efficiency is that external assets form a large portion of total assets of
the system and hence the liquidity effects are very strong.
Finally, we implement the feedback loops of risk transmission back from the sovereigns to the
banking system and study the effects of state aid on the complete model. The figures showing
results of this analysis (in the appendix) depict the number of failed banking subsystems in
dependence on state aid intensity and accounting for different levels of CDS sensitivity.
First, Figure 9 demonstrates the effects of bailouts and recapitalization. We see that the measure
has large impact on the banking system stability, which may be both positive and negative
depending on the initially shocked bank and CDS sensitivity setting. Generally, setting CDS
sensitivity equal to zero represents a situation in which the sovereigns are not negatively
affected by the state aid as increases in their deficits do not result in growth of their CDS spreads
and hence also growth of their implied probabilities of default. With non-zero CDS
sensitivities, the feedback loops are in their full function as higher deficit resulting from the
state aid increases the default probabilities of sovereigns. In case of bailouts and
recapitalization, when the CDS sensitivity is set to zero, the count of failed banking subsystems
is a decreasing function of the support intensity.
Figure 8: Asset relief effects
Source:
Secondly, looking at the effects of asset relief programmes as depicted in Figure 8A, we see
that they do not cause such sharp drops in numbers of failed banks as those of outright bailouts,
but still are very significant. Because asset relief is tied to the liquidity channel, we see that the
shape of the dependence of systemic stability on the support intensity (฀฀฀
) is similar to the
shape of its dependence on (1 − ฀).Also, in contrast to outright bailouts which may be targeted
to the initial propagator, in case of asset relief, the banks which are hit by the primary shock
always fail. Looking at the costs of this measure, Figure 8B shows that at the peak they are
higher than those of the bailouts. Also, except for the area of support intensity of 0.8 to 0.9
where they are smoother, they have very similar shape as the costs of bailouts. The reason for
asset relief to prove such efficiency is that external assets form a large portion of total assets of
the system and hence the liquidity effects are very strong.
Finally, we implement the feedback loops of risk transmission back from the sovereigns to the
banking system and study the effects of state aid on the complete model. The figures showing
results of this analysis (in the appendix) depict the number of failed banking subsystems in
dependence on state aid intensity and accounting for different levels of CDS sensitivity.
First, Figure 9 demonstrates the effects of bailouts and recapitalization. We see that the measure
has large impact on the banking system stability, which may be both positive and negative
depending on the initially shocked bank and CDS sensitivity setting. Generally, setting CDS
sensitivity equal to zero represents a situation in which the sovereigns are not negatively
affected by the state aid as increases in their deficits do not result in growth of their CDS spreads
and hence also growth of their implied probabilities of default. With non-zero CDS
sensitivities, the feedback loops are in their full function as higher deficit resulting from the
state aid increases the default probabilities of sovereigns. In case of bailouts and
recapitalization, when the CDS sensitivity is set to zero, the count of failed banking subsystems
is a decreasing function of the support intensity.
Source: Authors
Secondly, looking at the efects of asset relief programmes as depicted in Figure 8A, we
see that they do not cause such sharp drops in numbers of failed banks as those of outright
bailouts, but still are very signiicant. Because asset relief is tied to the liquidity channel,
we see that the shape of the dependence of systemic stability on the support intensity
() is similar to the shape of its dependence on . Also, in contrast to outright bailouts which
may be targeted to the initial propagator, in case of asset relief, the banks which are hit
by the primary shock always fail. looking at the costs of this measure, Figure 8B shows
that at the peak they are higher than those of the bailouts. Also, except for the area of
support intensity of 0.8 to 0.9 where they are smoother, they have very similar shape as
the costs of bailouts. the reason for asset relief to prove such eiciency is that external
assets form a large portion of total assets of the system and hence the liquidity efects
are very strong.
5.4 Efect of Feedback Loops
Finally, we implement the feedback loops of risk transmission back from the sovereigns to
the banking system and study the efects of state aid on the complete model. the igures
showing results of this analysis (in the appendix) depict the number of failed banking
subsystems in dependence on state aid intensity and accounting for diferent levels of
CdS sensitivity.
First, Figure 9 demonstrates the efects of bailouts and recapitalization. We see that the
measure has large impact on the banking system stability, which may be both positive and
negative depending on the initially shocked bank and CdS sensitivity setting. Generally,
setting CdS sensitivity equal to zero represents a situation in which the sovereigns are not
negatively afected by the state aid as increases in their deicits do not result in growth
of their CdS spreads and hence also growth of their implied probabilities of default. With
ActA všfs, 1/2014, vol. 882
non-zero CdS sensitivities,16
the feedback loops are in their full function as higher deicit
resulting from the state aid increases the default probabilities of sovereigns. in case of
bailouts and recapitalization, when the CdS sensitivity is set to zero, the count of failed
banking subsystems is a decreasing function of the support intensity.
When large subsystems having high systemic importance (France, Germany, the United
States and the United Kingdom) are initially shocked, the efects of support come only at
relatively high support intensity as the systemic break-down is prevented only at bailouts
ratio exceeding 50%. Moreover, for these countries’ subsystems, the number of defaults
is never signiicantly higher with the state support than without it, even though at CdS
sensitivities of 1.5 and 3 the positive efects come much later at higher support intensity
levels. if other banking subsystems are targets of the initial shock, we see that at non-zero
CdS sensitivities, the default count usually increases in the middle of the support intensity
interval as the state aid is still insuicient to signiicantly support the banks but already
weakens the sovereigns. this pattern is visible throughout the majority of the initiallyhit
banking systems. Also, even at non-zero CdS sensitivity levels, in case of almost all
initial propagators, the system is better of with full state support than without it. the
only exception is Belgium, Brazil and Greece, where state support clearly worsens the systemic
crisis. the reason is that they are neither too large nor too interconnected systems
and supporting them after they are initially hit only adds another channel of contagion
through a sovereign crisis.
third, Figure 10 shows the efect of asset relief. in case of zero CdS sensitivity, the positive
efects of this measure are less signiicant than in the case of bailouts. on the other hand,
as the CdS sensitivity progresses to higher values, the situation stays very similar and thus
for high CdS sensitivity cases, this measure would seem as the most itting one. However,
we suppose that this result is somewhat biased because of the dataset employed. First,
high portion of external assets in the system results in overestimating the measure’s effectiveness.
Moreover, the linkages between sovereigns and their non-domestic banks
form a minor portion of the total sovereign assets and each country’s banking system is
aggregated into a single agent. As a result, even though the sovereign which is performing
the asset relief programme is severely weakened, its default afects mainly its already
failed domestic banking system. if an interbank dataset that more precisely captures the
reality was available, we expect this measure to perform signiicantly worse than bailouts
and recapitalization.
Conclusions
in this paper, we focused on the link between systemic risk and sovereign crises. We modelled
how state support may inluence a distressed inancial system on a model calibrated
to 4Q 2011 data collected from several sources. our model contributes methodologically
to agent-based modelling of systemic stability by adding the sovereign sector and the
mechanisms of risk transfer between the banks and the sovereigns.
16 Our choice of CDS sensitivity values of 1.5 and 3 in the figures is in line with econometric studies such as Sand
(2012) or Cottarelli & Jaramillo (2012).
ActA všfs, 1/2014, vol. 8 B83
the model implements two types of state support to banks: bailout and asset relief. in the
short run when the feedback loops are not yet implemented, the efects of both measure
types are positive. in the longer run after implementation of the feedback loops through
sovereign defaults on bonds held by the banks, we found that a support measure’s real eficiency
depends on the measure intensity and CdS sensitivity, i.e. the market perception
of the increase in sovereign risk. these efects were the most pronounced in case of bailouts
and recapitalization, which according to our simulations may signiicantly improve
the systemic stability. However, with higher CdS sensitivity, it depends on which country
is initially hit: in case of banking systems that are systemically important, bailouts are effective
throughout the whole support intensity interval, whereas for the banks with lower
systemic importance, the support may actually worsen the situation. table 3 provides the
complete overview of the feedback loops analysis.
in general, the model proves that in the short run without the feedback loops, state aid
may signiicantly support the system and in the longer run with the feedback loop efects,
it may be efective or harmful depending on the system’s parameters. Moreover, the results
are indeed diferent for each individual type of state aid.
Table 3: impact of individual support measures on a calibrated model
Measure Description
Bailouts
and
recapitalization
• At zero CDS sensitivity, the count of failed banks is a decreasing function of support intensity on its
whole interval
• For systemically important subsystems, state support always improves systemic stability, even though
it is efective only at relatively high support intensity.
• At higher CDS sensitivities and in the middle of the support intensity interval, the efects are:
- Negative when the initially failed subsystem has lower systemic importance
- Neutral when the initially shocked subsystem is systemically important, the efects come in the
second half of the support intensity interval
• At full support intensity, the measure has a positive efect for all countries except for Belgium, Brazil
and Greece
Asset relief
• Eicient at the whole support intensity interval
• At zero CDS sensitivity the efects are less pronounced than in case of bailouts but still signiicant
• At non-zero CDS sensitivity levels, the positive efects stay signiicant
•The model is likely to overestimate this measure’s eiciency due to the dataset employed. However,
currently there is no better data on interbank exposures available
Source: Authors
Also, we found that majority of the total assets in our system are constituted by external
assets. this points out the shortcomings of studies that examine the systemic stability only
on the BiS interbank network data such as Chan-lau (2010), as this dataset amounts only
to a small fraction of the total banking assets. it stressed the need for deeper analysis and
more data availability on the structure of the interbank and state-bank exposures.
Finally, because of the agent-based modelling approach, we may extend our model in the
future with other types of inancial market agents such as large multinational institutions,
pension funds, insurance companies or even individual depositors. Moreover, we may add
ActA všfs, 1/2014, vol. 884
the real economy along with its input/output lows and observe the efects on individual
sectors when one sector is hit by a credit crunch or a drop in output. the lexibility and
extensibility of our modelling approach is another strong beneit, which may lead to many
more conclusions in the future research.
Acknowledgment
this research was supported by the Czech Science Foundation (project GACr No. 14-
02108S - the nexus between sovereign and bank crises) and by University of Economics
in Prague (project No. VŠE iP100040).
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Contact address
PhDr. Tomáš Klinger (corresponding author)
Charles University in Prague / Univerzita Karlova v Praze
institute of Economic Studies, Faculty of Social Sciences / institut ekonomických studií,
Fakulta sociálních věd
(tomas.klinger@seznam.cz)
PhDr. Petr Teplý, Ph.D.
University of Economics in Prague / Vysoká škola ekonomická v Praze
Faculty of Finance and Accounting / Fakulta inancí a účetnictví
(petr.teply@vse.cz)
ActA všfs, 1/2014, vol. 8 B87
Appendix
Figure 9: Bailouts and recapitalization with feedback loops	Bailouts	and	recapitalization	with	feedback	loops	
Source:
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ActA všfs, 1/2014, vol. 888
Figure 10: Asset relief with feedback loops on the calibrated model	Asset	relief	with	feedback	loops	on	the	calibrated	model	
Source:
Source: Authors