A Bayesian Methodology for Systemic Risk Assessment in Financial Networks

We develop a Bayesian methodology for systemic risk assessment in financial networks such as the interbank market. Nodes represent participants in the network, and weighted directed edges represent liabilities. Often, for every participant, only the total liabilities and total assets within this network are observable. However, systemic risk assessment needs the individual liabilities. We propose a model for the individual liabilities, which, following a Bayesian approach, we then condition on the observed total liabilities and assets and, potentially, on certain observed individual liabilities. We construct a Gibbs sampler to generate samples from this conditional distribution. These samples can be used in stress testing, giving probabilities for the outcomes of interest. As one application we derive default probabilities of individual banks and discuss their sensitivity with respect to prior information included to model the network. An R package implementing the methodology is provided. History: Accepted by Noah Gans, stochastic models and simulation. Supplemental Material: The online supporting document is available at https://doi.org/10.1287/ mnsc.2016.2546. Keywords: financial network * unknown interbank liabilities * systemic risk * Bayes * MCMC * Gibbs sampler * power law
1. Introduction Assessing systemic risk in financial systems is a key concern for regulators and policy makers. We think of systemic risk as the risk that some external or economic [...]