Computation of systemic risk measures: a mixed-integer programming approach

TL;DR

This paper develops a mixed-integer programming approach to compute systemic risk measures in complex financial networks, addressing non-convexities and providing theoretical and computational insights.

Contribution

It introduces a mixed-integer programming formulation for systemic risk measures in models with unrestricted cash flows, extending existing network models.

Findings

The proposed model effectively computes clearing vectors in complex networks.

The systemic risk measure can be non-convex due to binary variables.

Sensitivity analysis reveals parameter impacts on systemic risk measures.

Abstract

Systemic risk is concerned with the instability of a financial system whose members are interdependent in the sense that the failure of a few institutions may trigger a chain of defaults throughout the system. Recently, several systemic risk measures have been proposed in the literature that are used to determine capital requirements for the members subject to joint risk considerations. We address the problem of computing systemic risk measures for systems with sophisticated clearing mechanisms. In particular, we consider an extension of the Rogers-Veraart network model where the operating cash flows are unrestricted in sign. We propose a mixed-integer programming problem that can be used to compute clearing vectors in this model. Due to the binary variables in this problem, the corresponding (set-valued) systemic risk measure fails to have convex values in general. We associate nonconvex vector optimization problems with the systemic risk measure and provide theoretical results related to the weighted-sum and Pascoletti-Serafini scalarizations of this problem. Finally, we test the proposed formulations on computational examples and perform sensitivity analyses with respect to some model-specific and structural parameters.