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.