Systemic Losses Due to Counterparty Risk in a Stylized Banking System

Journal of Statistical Physics, Jun 2014

We report a study of a stylized banking cascade model investigating systemic risk caused by counterparty failure using liabilities and assets to define banks’ balance sheet. In our stylized system, banks can be in two states: normally operating or distressed and the state of a bank changes from normally operating to distressed whenever its liabilities are larger than the banks’ assets. The banks are connected through an interbank lending network and, whenever a bank is distressed, its creditor cannot expect the loan from the distressed bank to be repaid, potentially becoming distressed themselves. We solve the problem analytically for a homogeneous system and test the robustness and generality of the results with simulations of more complex systems. We investigate the parameter space and the corresponding distribution of operating banks mapping the conditions under which the whole system is stable or unstable. This allows us to determine how financial stability of a banking system is influenced by regulatory decisions, such as leverage; we discuss the effect of central bank actions, such as quantitative easing and we determine the cost of rescuing a distressed banking system using re-capitalisation. Finally, we estimate the stability of the UK and US banking systems comparing the years 2007 and 2012 by using real data.

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Systemic Losses Due to Counterparty Risk in a Stylized Banking System

Annika Birch Tomaso Aste We report a study of a stylized banking cascade model investigating systemic risk caused by counterparty failure using liabilities and assets to define banks' balance sheet. In our stylized system, banks can be in two states: normally operating or distressed and the state of a bank changes from normally operating to distressed whenever its liabilities are larger than the banks' assets. The banks are connected through an interbank lending network and, whenever a bank is distressed, its creditor cannot expect the loan from the distressed bank to be repaid, potentially becoming distressed themselves. We solve the problem analytically for a homogeneous system and test the robustness and generality of the results with simulations of more complex systems. We investigate the parameter space and the corresponding distribution of operating banks mapping the conditions under which the whole system is stable or unstable. This allows us to determine how financial stability of a banking system is influenced by regulatory decisions, such as leverage; we discuss the effect of central bank actions, such as quantitative easing and we determine the cost of rescuing a distressed banking system using re-capitalisation. Finally, we estimate the stability of the UK and US banking systems comparing the years 2007 and 2012 by using real data. - claims on the interbank market to other banks. The risk that banks impose on others through interconnectedness is called counterparty risk [51] and it is the subject of this paper. In this study, we are reporting how interconnectedness via the interbank market and the ratios between liabilities and assets influence the stability of a stylized banking system. The risk of banks to cause system failure is called systemic risk [24]. Extending a simple Merton model of default [44], we are able to test the systemic resilience of the financial system based on balance sheet quantities and determine ratios at which counterparty risk can cause the entire system to fail. There is a rich literature on stylized banking models. For instance, in [11,30,42,46] counterparty risk exposed via interbank lending is investigated. Other studies by [16,49,50], considered default cascade from an initial shock on asset prices and study market risk of correlated asset classes. These models have been used to investigate avalanches, loss distributions and parameter influences on the stability of the system. Most of the models are simulation based, and use as initial shock an arbitrary failure of a portion of banks, or arbitrary loss on the value of assets. In this paper, we propose a model combing the balance sheet based model, used by [30] and [46], with the contagion model used by [49] creating a stylized banking system that is analogous to the random field Ising model, a well-known model in the statistical physics literature. The application of this kind of model in the context of economic and financial behaviour has been reviewed in [14], and its application to credit default models has been discussed in [36]. In our stylized banking system, a bank is considered insolvent, if its liabilities are larger than the banks assets, the so-called balance sheet test [32]. Such insolvency of a bank can be triggered by a random event (such as changes in the value of the assets). The interconnectedness between institutions, in form of loans from one institution to another, can propagate this insolvency from a bank to another creating further insolvencies, bringing down -eventuallythe entire system. In this paper, we discuss a solution of this model, obtained by homogenizing the system. This allows for a mean-field assumption enabling us to compute the equilibrium fraction of surviving banks given changes in the values of the balance sheet quantities. Further, we test numerically our results changing the structure of the exposure network testing robustness and generality of the mean-field solution. We detail the parameter ranges that lead to a stable or unstable system, allowing us to determine restricting ratios between liabilities and assets to ensure a stable banking system. Further, we quantify the costs of potential rescue attempts to re-direct an unstable system into a stable region. We find that interbank lending can increase the stability of a banking system but this at the price of an increasing risk of a sudden systemic failure with inflating recovery cost. Finally we show, using balance sheet data for 2007 and 2012, that the US and UK banking system in 2007 was more prone to failure than in 2012. The structure of the paper is as follows: In Sect. 2, we describe the setup of the contagion model. This is followed by Sect. 3, where we state our assumptions and define an iteration function that describes the contagion process. In Sect. 4, we discuss the results and implications of the model. In particular, Sect. 4.4 addresses the stability of the system and discusses the implication for (...truncated)


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Annika Birch, Tomaso Aste. Systemic Losses Due to Counterparty Risk in a Stylized Banking System, Journal of Statistical Physics, 2014, pp. 998-1024, Volume 156, Issue 5, DOI: 10.1007/s10955-014-1040-9