An Axiomatic Viewpoint on the Rogers--Veraart and Suzuki--Elsinger Models of Systemic Risk

TL;DR

This paper introduces a comprehensive model of systemic risk in interbank networks that incorporates crossholdings and default charges, providing new computational methods for analyzing clearing solutions.

Contribution

It combines features of existing models and develops novel algorithms using mixed integer-linear programming and Gaussian elimination for systemic risk analysis.

Findings

Developed a finite family of fixpoint problems parameterized by binary vectors.

Created methods to compute maximal and minimal clearing pairs.

Integrated features from multiple systemic risk models.

Abstract

We study a model of clearing in an interbank network with crossholdings and default charges. Following the Eisenberg--Noe approach, we define the model via a set of natural financial regulations including those related with eventual default charges and derive a finite family of fixpoint problems. These problems are parameterized by vectors of binary variables. Our model combines features of the Ararat--Meimanjanov, Rogers--Veraart, and Suzuki--Elsinger networks. We develop methods of computing the maximal and minimal clearing pairs using the mixed integer-linear programming and a Gaussian elimination algorithm.