The influence of counterparty risk on financial stability in a stylized banking system

In this thesis, we investigate the influence of counterparty risk on financial stability in a banking system. Banks are exposed among each other via loans, credit derivatives, repayment agreements, commercial bonds and other financial products. Losses caused by counterparty failure can potentially result in a bank’s insolvency since a bank cannot expect to retrieve the full value of any obligation to an insolvent counterparty. The interconnectedness between institutions, in the form of exposure from one institution to another, can propagate insolvency from one bank to another, create further insolvencies, and eventually bring down the entire financial system. We study a cascade counterparty risk model of interacting banks using liabilities and assets to define banks’ balance sheets, which are further divided into interbank assets and liabilities, modelling direct dependencies between banks. We further assume that the balance sheet parameters are random variables. We simplify the system by assuming that banks can be in two states: solvent or insolvent. The state of a bank changes from solvent to insolvent whenever its liabilities are larger than the bank’s assets, the so-called balance sheet test of insolvency. This creates a stylized banking system that is analogous to the Random Field Ising model, a well-known model in the statistical physics literature. We solve the counterparty risk model semi-analytically by applying a mean-field assumption that homogenizes the banking system for different location-scale distributions. We call this simplified version of the counterparty risk model the mean-field model. The mean-field assumption allows us to conduct an analysis of the balance sheet parameters to evaluate the stability of the banking system. We observe the development of a fragile state where small perturbations to banks’ capital reserves can trigger a sudden system failure. The parameter analysis further allows us to calculate minimum capital requirements for banks ensuring a stable system, and to quantify the cost of rescuing a defaulted banking system. Two simulation models are used to test for the robustness of the results of the mean-field model. For the first simulation model, we consider a highly stylized banking system and verify that the mean-field model is robust for a variety of standard network topologies and random distributions. More specifically, we find that the interbank network is essential for the insolvency propagation. However, the structure of the interbank network does not play a critical role for the distribution of counterparty insolvency. We further show that diversification does not necessary reduce the risk of system failure. We also compute the critical balance sheet values for the stylized banking system in the mean-field model, at which the fragile state occurs. For the second simulation model, we use UK regulatory data to initialize the model. We show that a more realistic heterogeneous system with different bank types and a complex underlying interbank network calibrated on UK data also has systemic failures around similar sized shocks to banks’ capital as computed for the stylized homogeneous system. A network analysis on the exposure networks created using regulatory reports reveals a core-periphery topology with large internationally operating banks in the center of the exposure network and smaller regional banks in the periphery. By aggregating the fraction of surviving banks to specific bank types, we show that the behaviour of banks towards failure is independent of the size of their balance sheets or their position in the interbank network. This shows that bank-size heterogeneity and network complexity play a marginal role in the mechanism leading to systemic failure. However, we also observe significant differences. Insolvencies in the heterogeneous system start at smaller sized shocks than in the homogeneous system, and the residual fraction of surviving banks ends at a larger value in the heterogeneous system than in the homogeneous system. In conclusion, we demonstrate that a simple counterparty risk model replicates the behaviour of more complex simulation-based stress test models of a heterogeneous banking system. This is significant because it allows for a better understanding of the spread of system-wide insolvency, to draw policy implications such as the cost of rescuing an insolvent banking system, and to specify capital requirements that ensure a stable banking system that can be computed analytically using the mean-field model.