Using Shapley's Asymmetric Power Index to Measure Banks' Contributions to Systemic Risk

Abstract

An individual bank can put the whole banking system at risk if its losses in response to shocks push losses for the system as a whole above a critical threshold. We determine the contribution of banks to this systemic risk using a generalisation of the Shapley value; a concept originating in co-operative game theory. An important feature of this approach is that the order in which banks fail in response to a shock depends on the composition of the banks’ asset portfolios and capital buffers. We show how these factors affect banks’ contributions to systemic risk, and the extent to which these contributions depend on the level of the critical threshold.

Keywords: Shapley value, systemic risk, bank regulation

JEL Classification: C71, G01, G21, G28