Network structure indirect losses and financial contagion in inhomogeneous stochastic interbank networks

Abstract

We introduce new tiered bank network structures, allowing for many di erent bank sizes, and compare risk propagation in these structures with the well-known Erd˝os-R´enyi, assortative and disassortative structures. The simulations indicate that in the presence of market sentiment and liquidity e ects, the details of the structures in combination with the distribution of assets, the system’s interconnectedness and its size are crucially important in determining the risk of major capital loss in the network. In fact, even networks with similar levels of tiering can behave markedly di erent depending on these factors. In the absence of market sentiment and liquidity e ects, the di erences between the network structures is smaller. This highlights the importance of considering the network structure in conjunction with network characteristics, market sentiment and liquidity e ects. This implies that policy actions aimed at influencing a network’s characteristics must consider all aspects unique to that particular system and cannot follow a ‘one-size-fits-all’ approach. The framework is illustrated with an application using South African bank balance sheet data. Spikes in simulated assessments of systemic risk agree closely with spikes in documented subjective assessments of this risk. This indicates that network models can be useful for monitoring systemic risk levels. In a large network setting, the study then considers the fraction of nodes that default in stochastic, inhomogeneous financial networks following an initial shock to the system. Results for deterministic sequences of networks are generalized to stochastic networks to account for interbank lending relationships that change frequently. A general class of inhomogeneous stochastic networks is proposed for use in systemic risk research, and we illustrate how results that hold for Erd˝os-R´enyi networks can be generalized to the proposed network class. The network structure of a system is determined by interbank lending behaviour which may vary according to the relative sizes of the banks. We then use the results to illustrate how network structure influences the systemic risk inherent in large banking systems.