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

TL;DR

This paper investigates how interdependencies in financial networks can cause multiple equilibrium outcomes, including credit freezes, and derives conditions and bailout strategies to ensure systemic solvency.

Contribution

It provides necessary and sufficient conditions for bank solvency, characterizes minimal bailout payments, and analyzes computational complexity in various network structures.

Findings

Multiple equilibria occur due to dependency cycles.

Bailout injections to eliminate credit freezes are fully recoverable.

The minimum bailout problem is computationally hard, with solutions in specific network structures.

Abstract

We analyze how interdependencies between organizations in financial networks can lead to multiple possible equilibrium outcomes. A multiplicity arises if and only if there exists a certain type of dependency cycle in the network that allows for self-fulfilling chains of defaults. We provide necessary and sufficient conditions for banks' solvency in any equilibrium. Building on these conditions, we characterize the minimum bailout payments needed to ensure systemic solvency, as well as how solvency can be ensured by guaranteeing a specific set of debt payments. Bailout injections needed to eliminate self-fulfilling cycles of defaults (credit freezes) are fully recoverable, while those needed to prevent cascading defaults outside of cycles are not. We show that the minimum bailout problem is computationally hard, but provide an upper bound on optimal payments and show that the problem has intuitive solutions in specific network structures such as those with disjoint cycles or a core-periphery structure.