Credit Freezes, Equilibrium Multiplicity, and Optimal Bailouts in Financial Networks

Abstract

We analyze how interdependencies in financial networks can lead to self-fulfilling insolvencies and multiple possible equilibrium outcomes. We show that multiplicity arises if and only if there exists a certain type of dependency cycle in the network, and characterize banks' defaults in any equilibrium. We use this analysis to show that finding the cheapest bailout policy that prevents self-fulfilling insolvencies is computationally hard (and hard to approximate), but that the problem has intuitive solutions in specific network structures. Bailouts have an indirect value as making a bank solvent improves its creditors' balance sheets and reduces their bailout costs. We show that an algorithm that leverages these indirect benefits ensures systemic solvency at a cost that never exceeds half of the overall shortfall. In core-periphery networks, it is often optimal to bail out peripheral banks first as opposed to targeting core banks directly.

Keywords: Financial Networks, Markets, Systemic Risk, Financial Crisis, Networks, Banks, Credit Freeze, Default Risk, Financial Interdependencies

JEL Classification: D85, F15, F34, F36, F65, G15, G32, G33, G38