Failure and Rescue in an Interbank Network

This paper is concerned with systemic risk in the interbank market. We model this market as a directed graph in which the banks represent the nodes and the liabilities between the banks represent the edges. Our work builds on the modelling paradigm of Eisenberg and Noe (2001), extending it by introducing default costs in the system. We provide a rigorous analysis of those situations in which banks have incentives to bailout distressed banks. Such incentives exist under very mild conditions. We illustrate our results with some simple examples, and go on to discuss possible measures of soundness of a financial system, together with possible policy implications for resolution of distress.