Failure and Rescue in an Interbank Network

This paper is concerned with systemic risk in an interbank market, modelled as a directed graph of interbank obligations. This builds on the modelling paradigm of Eisenberg and Noe [Eisenberg L, Noe TH (2001) Systemic risk in financial systems. Management Sci. 47(2):236-249] by introducing costs of default if loans have to be called in by a failing bank. This immediately introduces novel and realistic effects. We find that, in general, many different clearing vectors can arise, among which there is a greatest clearing vector, arrived at by letting banks fail in succession until only solvent banks remain. Such a collapse should be prevented if at all possible. We then study situations in which consortia of banks may have the means and incentives to rescue failing banks. This again departs from the conclusions of the earlier work of Eisenberg and Noe, where in the absence of default losses there would be no incentive for solvent banks to rescue failing banks. We conclude with some remarks about how a rescue consortium might be constructed.