A Guide to IMF Stress Testing

Chapter 13. Introduction to the Network Analysis Approach to Stress Testing

Li Ong
Published Date:
December 2014
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Marco A. Espinosa-Vega and Juan Solé 

The global financial crisis that erupted in 2007 prompted policymakers and financial stability practitioners to intensify their search for a better understanding of how and when financial linkages could pose systemic risks. Hence, it is not surprising that there has been a surge of work in this area seeking to address some of the key conceptual aspects of financial interconnectedness. However, an ongoing challenge for policymakers has been the difficulty in turning rather theoretical proposals into methodologies that can be applied to detect and assess important linkages on an ongoing basis.

One method that is receiving renewed attention is network analysis. This approach allows the design of contagion and vulnerability metrics that are relatively easy to implement and interpret, and it potentially can be combined with traditional stress testing techniques to study contagion effects. In an effort to develop and strengthen the IMF’s financial surveillance capabilities, Espinosa-Vega and Solé (2011a) developed a network analysis tool that is capable of measuring direct and indirect systemic interconnectedness. We briefly discuss the rationale for using network analysis to conduct financial surveillance and provide a succinct review of the concept and some of the pertinent literature.1

Identifying vulnerabilities arising from systemic linkages is important in an increasingly intricate and complex international financial system. In times of stress, metrics from this analysis can help policymakers decide which institutions could be too interconnected to fail. More important, a proactive application of this analysis during tranquil times could help in regulating and containing specific institutions’ contribution to systemic risk (see Espinosa-Vega and Solé, 2011b).

What is Network Analysis?

Network analysis is the mapping and measuring of relationships and flows within a group of agents. Thus defined, the nodes in a network represent agents (e.g., financial institutions, people, computers), while the links show relationships or flows between nodes (e.g., exchange of cash, messages, information). The main advantage of network analysis is that it provides both a visual and a mathematical analysis of relationships, from which answers to key questions about the characteristics and performance of the network can be obtained.

To illustrate, let us consider an early example from the social networks literature by David Krackhardt—the kite network (Figure 13.1). This network comprises a group of 10 friends (nodes) who communicate among themselves (exchange messages—represented by links). We could be interested, for example, in finding out which persons are more popul ar and whether some have friends outside the core group. Focusing individually on each agent (e.g., by interviewing him or her) may give us some information about his or her relationships. For instance, we may discover that the person called Diane talks to as many as six people in the group, whereas Heather talks only to three. This may lead us to conclude that Diane is more important than Heather in terms of guaranteeing that messages are delivered to all members of the group. But to fully exploit the information gathered—and to have a proper understanding of the group dynamics—we need a tool that can provide structure to these relationships. Only then can we answer important questions about, for instance, an agent’s relative importance within the group (e.g., his or her popularity); the speed at which a message can be delivered to all members in the group; or what possible communication failures there may be that could cause a message to never reach certain agents.

Figure 13.1The Kite Network

Applying network analysis to our example, it is clear that Diane is the agent with the higher number of connections. However, her failure to repeat a message would not imply that information stalls within the network. Consider instead the role played by Heather—if she is removed from the information flow, Ike and Jane’s communication with the rest would break down. In technical terms, Diane has the highest degree in the network, whereas Heather has the highest betweenness. Degree is a measure that reflects a node’s relative number of ties to other nodes, whereas betweenness measures the extent to which a node lies between other nodes, taking into account the connectivity of the node’s neighbors and giving a higher value for nodes bridging clusters.2

The relevance of network analysis for financial stability analysis is immediately apparent if one reconsiders the above example imagining that each node is a bank receiving and/or giving funding to other banks. Thus, the application of network analysis to a banking system that had a kite structure would reveal that although Bank Diane is a central player in the network, Bank Heather is vital for the funding operations of Bank Ike and Bank Jane. Indeed, after the failure of Bank Heather, Bank Jane may not be able to survive even though Banks Heather and Jane do not have a direct link.

In sum, the application of network analysis to financial surveillance is a powerful tool for identifying both potentially systemic and vulnerable institutions in an objective manner, as well as for tracking potential contagion paths. For example, we would see that the failure of Bank Heather would first lead to the failure of Bank Ike and then the failure of Bank Jane. It should be emphasized, however, that network analysis constitutes only one element in the financial stability tool kit. In fact, network analysis could be combined with regular stress testing exercises in order to gain a more comprehensive and clearer picture of vulnerabilities in a given banking system. For instance:

  • Traditional stress tests could be run to identify the types of shocks that could have the largest first-round effects on individual institutions (Figure 13.2). Once these shocks are determined, they could be fed into a network model to assess second- (and higher) round effects.

  • Conversely, network analysis could begin by applying a first set of shocks to the financial system in order to identify those institutions that are more systemic (i.e., whose failure would have the largest contagion impact) and those that are most vulnerable (i.e., most susceptible to failure) and then proceed with a more thorough stress test of some selected institutions.

Figure 13.2Interface between Network Analysis and Stress Testing

Source: Authors.

Applications to Financial Stability

Most of the initial applications of network analysis to financial surveillance were aimed at assessing the stability of domestic banking systems. In broad terms, the basis of these studies was the construction of a matrix of interbank exposures that identified gross lending and borrowing among institutions, in order to then simulate shocks to specific institutions and track domino effects to other institutions within that particular financial system.3 Some of the main findings of this literature are that (1) even though contagion owing to credit shocks seems likely to be rare, (2) whenever contagion takes place, it carries a high cost for the financial system. It should be said, however, that in part the low incidence of contagion in these papers could arise because most simulations ignore liquidity shocks and credit risk transfers (e.g., derivatives)—both of which have been shown to be important sources of potential contagion. Another potential problem with some of these results is the reliance on certain estimation techniques (i.e., maximum entropy) to complete data sets, which tend to ignore the role of relationship lending among financial institutions and thus underestimate the concentration of potential exposures.4

Largely triggered by the crisis, there has been a second wave of research applying network analysis to the international context.5 Most of these papers have relied on data from the Bank for International Settlements in order to study the topology of the international banking network as well as the potential cross-border contagion paths arising from shocks to a particular financial system. Taken as a whole, these papers provide important insights for international financial surveillance, as they reveal that (1) liquidity shocks—and not only credit shocks as mostly emphasized in the previous literature—can wreak havoc across the international financial network; (2) there are nowadays more (and smaller) financial systems (i.e., nodes) capable of triggering international contagion; and (3) the speed of propagation of contagion has increased in recent years.

The following two chapters in this volume on network analysis constitute an extension of the work begun in Chan-Lau and others (2009) and demonstrate how network analysis is used in IMF staff’s work:

  • Chapter 14 by Espinosa-Vega and Solä illustrates the application of network analysis to track the reverberation of credit and liquidity shocks throughout the global financial system and shows how these techniques can be applied to draw global risk maps that reveal systemic and vulnerable spots, as well as potential contagion paths. In addition, the chapter shows the importance of incorporating off-balance risk transfers in the assessment of cross-border financial linkages, as these financial instruments can severely alter the risk profile of entire financial systems. The authors propose an enriched simulation algorithm that is able to account for risk transfers.

  • Chapter 15 by Chan-Lau also shows the value of applying network techniques in a global setting to identify global sources of systemic risk, as well as regional ones. In addition, this chapter also illustrates a country case (Chile) using bank-specific disaggregated data to study potential intersectoral sources of risk. In exploiting supervisory data on individual banks’ claims vis-à-vis other domestic and foreign banks, as well as other nonbank financial institutions, the study shows that the main sources of domestic risk in the Chilean banking system are shocks that affect banks’ claims on households and domestic corporations, and to a lesser degree shocks emanating from Spanish and U.S. banks.

Policy Reflections

The global financial crisis reminds us that financial interconnectedness leads (rapidly and forcefully) to spillovers not only among banks but also to the nonbank financial sector, posing great risks to financial stability. Thus, financial regulators need to be equipped with the ability to improve their understanding and monitoring capability of direct and indirect linkages. Network analysis is one of the methods for doing so. That said, it is important to bear in mind that the application of network analysis to practical financial surveillance is still in a developmental stage and faces important challenges. Specifically:

  • It is still difficult, if not impossible, to obtain comprehensive information at an institutional level. Some of the areas where better data are needed include bank-level information on banks’ exposures and funding positions, with breakdowns by counterparty, currency, and remaining maturity. Fortunately, important progress is being made in this regard under the auspices of the Financial Stability Board (FSB) and IMF initiative on data gaps (FSB and IMF, 2009, 2011).

  • In addition, network analysis still needs to be expanded to incorporate factors such as the imperfect integration of global money markets arising from heterogeneous resolution regimes; and potential problems with derivative and collateral clearing mechanisms; and it should include more information on off-balance-sheet and shadow banking activities.

  • The existing literature does not yet include an adequate modeling of the endogenous response of institutions to shocks.

To conclude, globalization of financial activity means that it is close to impossible for a national regulator alone to undertake effective surveillance of potentially systemic linkages. Therefore, enhancing our understanding and monitoring of global systemic linkages requires a reliable method to assess financial connections, as well as strong information-sharing agreements on cross-market and cross-border linkages.


For an excellent Internet resource containing a wealth of information on network analysis, visit the Web site http://www.financialnetworkanalysis.com, maintained by Kimmo Soramäki.

A description of the computation of these (and other) network mea sures is beyond the scope of our introductory chapter. The interested reader can visit http://www.orgnet.com.

One of the main challenges faced in this line of study was the compilation of interbank exposures. This was attributable to a combination of factors, namely, that the data (1) may be available only to national supervisors; (2) are not collected in a systematic manner; and (3) are not publicly available. To circumvent these limitations, researchers often complemented available data with interpolations or estimations by different methods.

In broad terms, maximum entropy is akin to assuming the maximum possible diversification of exposures, thus minimizing the effect of concentration risk.

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