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

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Abstract

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.

Introduction

The recent financial crisis has shown that systemic risk takes many forms and is highly dynamic. It builds up slowly in normal times, and unwinds rapidly during times of distress. The insolvency of the US investment bank Lehman Brothers in September 2008 marked the tipping point between the build-up and rapid unwinding of systemic risks and led to a freeze in interbank markets. Banks were no longer able to obtain liquidity and engaged in costly fire sales. Central banks were forced to undertake unprecedented non-standard measures to ensure liquidity provision within the banking system.

This paper analyzes the non-trivial network structure of the bilateral interbank loans which form the money market. Interbank networks exhibit what Haldane (2009) describes as a knife-edge, or robust-yet-fragile property: in normal times the connections between banks lead to an enhanced liquidity allocation and increased risk sharing.1 In times of crisis, however, the same interconnections can amplify initial shocks such as the insolvency of a large and highly interconnected bank.2 This implies that there are two different regimes of financial stability: a stable regime in which initial shocks are contained, and a fragile regime in which initial shocks are transmitted via interbank linkages to a substantial part of the financial system. The knife-edge property of interbank markets can be attributed to a counterparty risk externality which is characteristic of over-the-counter markets (e.g. Acharya and Bisin (2010)). When a bank lends to a number of other banks it is oblivious to any links between those banks and might underestimate its portfolio correlation. A similar effect can be termed correlation externality and arises when a bank is oblivious to the asset holdings of other banks. The counterparty risk externality can lead to interbank contagion (sometimes called cascading defaults), while the correlation externality can lead to common shocks.3

This poses the question of whether there exist network structures that are less prone to systemic risk (caused by either externality) and hence more resilient to financial distress. The massive intervention of central banks at the height of the financial crisis furthermore raises the question of whether central bank interventions can effectively stabilize interbank markets and ensure banks’ liquidity provision. Finally, in order to understand systemic financial fragility, it is necessary to compare the instabilities caused by the counterparty risk externality with instabilities caused by the correlation externality (i.e. to compare the effects of interbank contagion to the effects of common shocks).

This paper addresses the aforementioned questions by developing a simple dynamic model of a banking system that explicitly incorporates an evolving interbank network structure. Banks optimize a portfolio of risky investments and riskless excess reserves. Risky investments are long-term investment projects that fund an unmodelled firm sector while riskless excess reserves are short-term and held at the deposit facility of the central bank.4 Banks face a stochastic supply of household deposits and stochastic returns from risky investments. This gives rise to liquidity fluctuations and initiates the dynamic formation of an interbank loan network. Banks, furthermore, have access to central bank liquidity if they can provide sufficient collateral.

Three key results are obtained. First, this model is used to compare different possible interbank network structures, and it is shown that in random graphs the relationship between the degree of interconnectivity and financial (in-)stability is non-monotonic. In times of distress, money centre networks (which are typically found in reality) are seen to be more stable than purely random networks. In tranquil times, however, I show that different interbank network structures do not have a substantial effect on financial stability. The key intuition behind this behaviour is a regime switching property of the model financial system. In tranquil times, liquidity demand-driven interbank lending is low and cascading defaults are thus contained. In times of crisis, individual banks suffer larger liquidity fluctuations and engage in higher liquidity-driven interbank lending. This drives the financial system as a whole into a contagious regime. When exactly the regime switching behaviour occurs depends on the interbank network structure.

Second, I show that the central bank can stabilize the financial system in the short run. In the long run, however, the system always converges to a steady state which depends, amongst other things, on the interbank network structure. Central bank liquidity provision helps banks to withstand liquidity shocks for a longer time. This, however, allows banks that would otherwise be insolvent to engage in liquidity demand-driven interbank borrowing. The result is that the financial system as a whole is more highly interconnected and more likely to enter the contagious regime.

Third, I show that the introduction of a common shock hitting all banks simultaneously can cause substantial financial fragility but has a less severe impact on the liquidity provision of the interbank market. This finding is of particular importance for policymakers implementing emergency measures in times of a crisis: while interbank contagion requires mainly liquidity provision, a common shock requires banks to be recapitalized.

The remainder of this paper is organized as follows. After this introduction, section two outlines the contribution to the literature. Section 3 describes the dynamic model that has been used to analyze the aforementioned questions. Section 4 will present the main results, Section 5 provides a discussion of further model implications, while sextion six concludes.

Section snippets

Relation to the literature

The literature on financial networks has been growing rapidly over the past few years.5 As a result, this paper relates to various strands of literature. First, it relates to a class of network models using static network structures and fixed balance sheets. In contrast to this literature the present paper models banks that optimize their balance sheet structure in every period and continuously adapt the

The model

This section develops a dynamic model of a banking system that can be used to analyze the impact of the interbank network structure on financial stability. First, deposit fluctuations have to be included: (i) Because of the maturity transformation that banks perform and since deposits usually have a short maturity, deposit fluctuations can lead to illiquidity. Banks which become illiquid have to liquidate their long-term investments at steep discounts. Due to marked-to-market accounting, these

Results

The three key questions that this paper answers are: (i) Are some network structures more resilient to systemic risk than others? (ii) Can central banks stabilize interbank markets? And (iii) How does a common shock to the banking capital of all banks interact with the counterparty risk externality? Each of these questions is addressed in turn.

Discussion

The model presented in this paper gives rise to a number of interesting questions that could be addressed, but are beyond the scope of the present paper.

Varying required reserves. This paper considers the effect of central bank policy on financial stability. In particular, it analyzes how central bank liquidity provision can prevent widespread default cascades. However, liquidity provision through open market operations and via the standing facilities is not the only tool available to central

Conclusion

This paper analyzes different forms of systemic risk in a dynamic multi-agent simulation with portfolio-optimizing banks that engage in bilateral interbank lending. Three key results are obtained. First, complementing the existing literature, which analyzes static interbank networks only, this paper shows that the interbank network structure does have a substantial impact on financial stability only in times of distress. Second, this paper also incorporates the central bank and shows that

Acknowledgements

The author wishes to thank Monica Billio (discussant), Domenico Delli Gatti (discussant), Giulia Iori, Dan Ladley, Markus Pasche, Christie Smith (discussant), Benjamin Tabak, and Tanju Yorulmazer, seminar participants at Deutsche Bundesbank, Banque de France, South African Reserve Bank, Bank of England, Oxford, Jaume I, Leicester, Stellenbosch, Pretoria, Office of Financial Research, Narodowy Bank Polski, City University, and Cambridge University, as well as conference participants at the

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