We consider the fraction of nodes that default in large, 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 Erdős–Rényi networks can be generalized to the proposed network class. The network structure of a system is determined by interbank lending behavior which may vary according to the relative sizes of the banks. We then use the results of the paper to illustrate how network structure influences the systemic risk inherent in large banking systems.

We present a network-based framework for simulating systemic risk that considers shock propagation in banking systems. In particular, the framework allows the modeller to reflect a topdown framework where a shock to one bank in the system affects the solvency and liquidity position of other banks, through systemic market risks and consequential liquidity strains. We illustrate the framework 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. The model results are sensitive to liquidity risk and market sentiment and therefore the related parameters are important considerations when using a network approach to systemic risk modelling.

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