Modelling the emergence of the interbank networks

Interbank contagion has become a buzzword in the aftermath of the financial crisis that led to a series of shocks to the interbank market and to periods of pronounced market disruptions. However, little is known about how interbank networks are formed and about their sensitivity to changes in key bank parameters (for example, induced by common exogenous shocks or by regulatory initiatives). This paper aims to shed light on these issues by modelling endogenously the formation of interbank networks, which in turn allows for checking the sensitivity of interbank network structures and hence, their underlying contagion risk to changes in market-driven parameters as well as to changes in regulatory measures such as large exposures limits. The sequential network formation mechanism presented in the paper is based on a portfolio optimization model, whereby banks allocate their interbank exposures while balancing the return and risk of counterparty default risk and the placements are accepted taking into account funding diversification benefits. The model offers some interesting insights into how key parameters may affect interbank network structures and can be a valuable tool for analysing the impact of various regulatory policy measures relating to banks’ incentives to operate in the interbank market.     

Assessing financial contagion in the interbank market: Maximum entropy versus observed interbank lending patterns

Interbank markets allow banks to cope with specific liquidity shocks. At the same time, they may represent a channel for contagion as a bank default may spread to other banks through interbank linkages. This paper analyses how contagion propagates within the Italian interbank market using a unique data set including actual bilateral exposures. Based on the availability of information on actual bilateral exposures for all Italian banks, the results obtained by assuming the maximum entropy are compared with those reflecting the observed structure of interbank claims. The comparison indicates that, under certain circumstances, depending on the structure of the interbank linkages, the recovery rates of interbank exposures and banks’ capitalisation, the maximum entropy approach overrates the scope for contagion.     

Credit Risk in Interbank Networks

ABSTRACT

One of the most striking characteristics of modern financial systems is their complex interdependence, comprising a network of bilateral exposures in the interbank market, in which institutions with surplus liquidity can lend to those with a liquidity shortage. Empirical studies reveal that some interbank networks have features of scale-free networks. We explore the characteristics of financial contagion in networks whose distribution of links approaches a power law, using a model that defines banks’ balance sheets from information on network connectivity. By varying the parameters for the creation of the network, several interbank networks are built, in which the concentration of debt and credit comes from the distribution of links. The results suggest that networks that are more connected and have a high concentration of credit are more resilient to contagion than other types of networks analyzed.     

The formation of financial networks

Modern banking systems are highly interconnected. Despite various benefits, linkages between banks carry the risk of contagion. In this article, I investigate whether banks can commit ex ante to mutually insure each other, when there is contagion risk in the financial system. I model banks' decisions to share this risk through bilateral agreements. A financial network that allows losses to be shared among various counterparties arises endogenously. I characterize the probability of systemic risk, defined as the event that contagion occurs conditional on one bank failing, in equilibrium interbank networks. I show that there exist equilibria in which contagion does not occur.     

A network model of systemic risk: stress testing the banking system1

Although there are many definitions of systemic risk, most agree that it manifests itself by an initial shock that results in the failure of one or more banks and then spreads out to the entire system by a contagion mechanism which can result in the failure of more banks in the system. Assuming that bank failures in the initial shock are randomly dependent on the failure probabilities of the individual banks and that the ensuing contagion process is deterministic, depending on interbank exposures, in this paper we propose a network model to analyse systemic risk in the banking system that, in contrast to other proposed models, seeks to obtain the probability distribution of losses for the financial system resulting from the shock/contagion process. Thus, calculating the probabilities of joint failures by simulation and assuming that the matrix of bilateral interbank exposures is known, we represent systemic risk in the financial system by means of a graph and use discrete modelling techniques to characterize the dynamics of contagion and corresponding losses within the network. The probability distribution of losses, risk profile for the Mexican banking system, is obtained through an efficient, complete enumeration procedure of all possible bank default events in the system. This, in turn, allows the use of the wide variety of well-established risk measures to describe the fragility of the financial system. Additionally, the model allows us to perform stress tests along both the bank default probabilities and the interbank exposures and is used to assess the risk of the Mexican banking system. Copyright © 2009 John Wiley & Sons, Ltd.     

Interbank Credit Lines as a Channel of Contagion

This paper assesses the potential for contagion in the Swiss interbank market using new data on bilateral bank exposures as well as on credit lines. A simulation approach is applied to assess the banking system's inherent instability. Moreover, the spill-over effects of a simulated default situation in the interbank market on the liquidity and solvency of banks are measured. The main findings are, first, that there is a substantial potential for contagion. Second, the exposure as well as the credit line contagion channel are relevant for Switzerland. Third, a lender of last resort intervention could reduce spill-over effects remarkably. Finally, the structure of the interbank market has considerable impact on its resilience against spill-over effects: Centralized markets are more prone to contagion than homogenous ones. JEL classification: C81, G21. The opinions expressed herein are my own and not those of the Swiss National Bank.     

Análisis de contagio en el sistema financiero mexicano combinando el modelo de Merton y redes aleatorias

The control of systematic risk and the contagion effect are very important on the regulation and Basilea context. This paper presents a two phase model (Merton Model on the first part and Random networks Erdös-Rényi in the second part) in order to analyze the contagion effect on the Mexican bank system. The conclusions are that the Banks could not be infected or fall into default depending of the behavior of liabilities, the structure of the network and (external asset/interbank asset) ratio and (capital/asset) ratio. The results are consistent with the regulation politics in order to avoid the contagion in Mexico Financial System.     

Credit Contagion from Counterparty Risk

Standard credit risk models cannot explain the observed clustering of default, sometimes described as "credit contagion." This paper provides the first empirical analysis of credit contagion via direct counterparty effects. We find that bankruptcy announcements cause negative abnormal equity returns and increases in CDS spreads for creditors. In addition, creditors with large exposures are more likely to suffer from financial distress later. This suggests that counterparty risk is a potential additional channel of credit contagion. Indeed, the fear of counterparty defaults among financial institutions explains the sudden worsening of the credit crisis after the Lehman bankruptcy in September 2008.     

(In)Efficient Interbank Networks

We study the efficiency properties of the formation of an interbank network. Banks face a trade-off by establishing connections in the interbank market. On the one hand, banks improve the diversification of their liquidity risk and therefore can obtain a higher expected payoff. On the other hand, banks not sufficiently capitalized have risk-shifting incentives that expose them to the risk of bankruptcy. Connecting to such risky banks negatively affects expected payoff. We show that both the optimal and the decentralized networks are characterized by a core-periphery structure. The core is made of the safe banks, whereas the periphery is populated by the risky banks. Nevertheless, the two network structures coincide only if counterparty risk is sufficiently low. Otherwise, the decentralized network is underconnected as compared to the optimal one. Finally, we analyze mechanisms that can avoid the formation of inefficient interbank networks.     

The effect of the interbank network structure on contagion and common shocks

This paper proposes a dynamic multi-agent model of a banking system with central bank. Banks optimize a portfolio of risky investments and riskless excess reserves according to their risk, return, and liquidity preferences. They are linked via interbank loans and face stochastic deposit supply. Comparing different interbank network structures, it is shown that money-centre networks are more stable than random networks. Evidence is provided that the central bank stabilizes interbank markets in the short run only. Systemic risk via contagion is compared with common shocks and it is shown that both forms of systemic risk require different optimal policy responses.     

Completeness,interconnectedness and distribution of interbank exposures—a parameterized analysis of the stability of financial networks

This paper assesses the impact of a certain structure of interbank exposures on the stability of a stylized financial system. Given a certain balance sheet structure of financial institutions, a large number of valid matrices of interbank exposures is created by a random generator. Assuming a certain loss given default, domino effects are simulated. The main results are, first, that financial stability depends not only on the completeness and interconnectedness of the network, but also on the distribution of interbank exposures within the system (measured by entropy). Second, looking at random graphs, the sign of the correlation between the degree of equality of the distribution of claims and financial stability depends on the connectivity of the financial system as well as on additional parameters that affect the vulnerability of the system to interbank contagion. Third, the more concentrated the assets are within a money center model, the less stable it is. Fourth, a money center model with asset concentration among core banks is less stable than a random graph with banks of homogeneous size.     

Assessing systemic risk using interbank exposures in the global banking system

This paper contributes to the literature on systemic risk by examining the network structure of bilateral exposures in the global banking system. The global interbank market constitutes a major part of the global banking system. The market has a hierarchical network structure, composed of the national or jurisdictional area's local markets and the cross-border interbank market. First, we estimate the bilateral exposures matrix using aggregate financial data on loans and deposits from Bankscope and analyze the interconnectedness in the market using network centrality measures. Subsequently, for the model analysis, we apply the Eisenberg–Noe framework to a multi-period setting. In this framework, bank defaults are classified into stand-alone defaults and contagious defaults. The banks in our sample (i.e., the top 202 banks with more than $50 billion in total assets) comprise a major part of this global banking system. The main findings are as follows: The theoretical network analysis using network centrality measures showed that most of the banks designated as global systemically important banks (G-SIBs) play a central role in the global interbank market. The theoretical default analysis showed a few contagious defaults triggered by the basic defaults during and after the global financial crisis. Our stress test proved that many G-SIBs theoretically caused 1–6 contagious defaults. Our methodology would assist in the development of a monitoring system by the respective supervisory authorities as well as in the implementation of bank-internal stress tests of default contagion.     

Macro-Networks: An application to euro area financial accounts

This paper develops a financial network, designated the “Macro-Network”, that depicts the connections between the main financial and non-financial sectors of the economy in the various financial instruments of the euro area. The Macro-Network comprises of linkages across financial and non-financial sectors in each country. These country-level sector networks are then connected by the cross-border links between the individual banking sectors. Using the Macro-Network to simulate financial shocks, we find that the propagation effects depend on the underlying network structure, which evolves over time. After the financial crisis, bilateral linkages contracted sharply, reflecting the surge in counterparty risk and the de-leveraging processes. Nonetheless, our analysis suggests that even after this process, vulnerabilities remained in the euro area financial system, while a more diversified portfolio of cross-border exposures might mitigate the shock effects. We identify sectors which are most relevant for the propagation of financial shocks in the Macro-Network.     

Fire Sales in a Model of Complexity

We present a model of financial crises that stem from endogenous complexity. We conceptualize complexity as banks' uncertainty about the financial network of cross exposures. As conditions deteriorate, cross exposures generate the possibility of a domino effect of bankruptcies. As this happens, banks face an increasingly complex environment since they need to understand a greater fraction of the financial network to assess their own financial health. Complexity dramatically amplifies banks' perceived counterparty risk, and makes relatively healthy banks reluctant to buy risky assets. The model also features a novel complexity externality.     

Mapping the UK interbank system

We present new evidence on the structure of interbank connections across key markets: derivatives, marketable securities, repo, unsecured lending and secured lending. Taken together, these markets comprise two networks: a network of interbank exposures and a network of interbank funding. Network structure varies across and within these two networks, for reasons related to markets’ different economic functions. Credit risk and liquidity risk therefore propagate in the interbank system through different network structures. We discuss the implications for financial stability.     

Optimal equity infusions in interbank networks

We study optimal equity infusions into a financial network prone to the risk of contagious failures, which may be due to insolvency or to bank runs by short term creditors. Bank runs can be triggered by failures of connected banks.Under complete information on interbank linkages, we show that the problem reduces to a combinatorial optimization problem. Subject to budget constraints, the government chooses the set of minimal cost whose survival induces the maximum network stability. Our results demonstrate that the optimal equity infusion might significantly mitigate failure contagion risk and stabilize the system. In the case of partial information on the network, the controllers’ focus swiftly changes from preventing insolvencies to preventing runs by short term creditors.     

Cross-border interbank networks,banking risk and contagion

Recent events have highlighted the role of cross-border linkages between banking systems in transmitting local developments across national borders. This paper analyzes whether international linkages in interbank markets affect the stability of interconnected banking systems and channel financial distress within a network consisting of banking systems of the main advanced countries for the period 1994–2012. Methodologically, I use a spatial modeling approach to test for spillovers in cross-border interbank markets. The results suggest that foreign exposures in banking play a significant role in channeling banking risk: I find that countries that are linked through foreign borrowing or lending positions to more stable banking systems abroad are significantly affected by positive spillover effects. From a policy point of view, this implies that in stable times, linkages in the banking system can be beneficial, while they have to be taken with caution in times of financial turmoil affecting the whole system.     

Credit Contagion Channels: Market Microstructure Evidence from Lehman Brothers’ Bankruptcy

Immediately after Lehman Brothers’ bankruptcy, many firms disclosed their financial exposure (or lack thereof) to Lehman. This offers a clean setting to test two credit contagion channels through which a financial firm's bankruptcy can affect other firms—“counterparty risk” and “information transmission” channels. Using market microstructure variables to measure the various dimensions of contagion effects, we provide robust evidence supporting the significance of counterparty risk. Firms with exposure to Lehman suffered more severe negative effects—wider bid‐ask spread, higher price impact, greater information asymmetry, and greater selling pressure—than unexposed firms. We find mixed evidence regarding the information transmission hypothesis.     

Time-varying integration,interdependence and contagion

Bekaert et al. (2005) define contagion as “correlation over and above what one would expect from economic fundamentals”. Based on a two-factor asset pricing specification to model fundamentally-driven linkages between markets, they define contagion as correlation among the model residuals, and develop a corresponding test procedure. In this paper, we investigate to what extent conclusions from this contagion test depend upon the specification of the time-varying factor exposures. We develop a two-factor model with global and regional market shocks as factors. We make the global and regional market exposures conditional upon both a latent regime variable and three structural instruments, and find that, for a set of 14 European countries, this model outperforms more restricted versions. The structurally-driven increase in global (regional) market exposures and correlations suggest that market integration has increased substantially over the last three decades. Using our optimal model, we do not find evidence that further integration has come at the cost of contagion. We do find evidence for contagion, however, when more restricted versions of the factor specifications are used. We conclude that the specification of the global and regional market exposures is an important issue in any test for contagion.     

Financial Networks: Contagion, Commitment, and Private Sector Bailouts

I develop a model of financial networks in which linkages not only spread contagion, but also induce private sector bailouts, where liquid banks bail out illiquid banks because of the threat of contagion. Introducing this bailout possibility, I show that linkages may be optimal ex ante because they allow banks to obtain some mutual insurance even though formal commitments are impossible. However, in some cases (e.g., when liquidity is concentrated among a small group of banks), the whole network may collapse. I also characterize the optimal network size and apply the results to joint liability arrangements and payment systems.