Optimal Clearing Payments in a Financial Contagion Model

TL;DR

This paper analyzes the clearing mechanism in financial networks, deriving conditions for unique solutions and proposing a method to reduce systemic risk by modifying payment rules, using convex optimization.

Contribution

It provides novel necessary and sufficient conditions for the uniqueness of clearing payments in arbitrary network topologies and suggests a systemic risk reduction approach by altering proportionality rules.

Findings

Derived conditions for clearing payment uniqueness.

Proposed convex optimization framework for systemic risk control.

Showed that lifting proportionality reduces system losses.

Abstract

Financial networks are characterized by complex structures of mutual obligations. These obligations are fulfilled entirely or in part (when defaults occur) via a mechanism called clearing, which determines a set of payments that settle the claims by respecting rules such as limited liability, absolute priority, and proportionality (pro-rated payments). In the presence of shocks on the financial system, however, the clearing mechanism may lead to cascaded defaults and eventually to financial disaster. In this paper, we first study the clearing model under pro-rated payments of Eisenberg and Noe, and we derive novel necessary and sufficient conditions for the uniqueness of the clearing payments, valid for an arbitrary topology of the financial network. Then, we argue that the proportionality rule is one of the factors responsible for cascaded defaults, and that the overall system loss can be reduced if this rule is lifted. The proposed approach thus shifts the focus from the individual interest to the overall system's interest to control and contain adverse effects of cascaded failures, and we show that clearing payments in this setting can be computed by solving suitable convex optimization problems.