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

Abstract

In the scope of nance, systemic risk is concerned with the instability of a nancial system, where the members of the system are interdependent in the sense that the failure of some institutions may trigger defaults throughout the system. National and global economic crises are important examples of such system collapses. One of the factors that contribute to systemic risk is the existence of mutual liabilities that are met through a clearing procedure. In this study, two network models of systemic risk involving a clearing procedure, the Eisenberg-Noe network model and the Rogers-Veraart network model, are investigated and extended from the optimization point of view. The former one is extended to the case where operating cash ows in the system are unrestricted in sign. Two mixed integer linear programming (MILP) problems are introduced, which provide programming characterizations of clearing vectors in both the signed Eisenberg-Noe and Rogers-Veraart network models. The modi cations made to these network models are nancially interpretable. Based on these modi cations, two MILP aggregation functions are introduced and used to de ne systemic risk measures. These systemic risk measures, which are not necessarily convex set-valued functions, are then approximated by a Benson type algorithm with respect to a user-de ned error level and a user-de ned upper-bound vector. This algorithm involves approximating the upper images of some associated non-convex vector optimization problems. A computational study is conducted on two-group and three-group systemic risk measures. In addition, sensitivity analyses are performed on twogroup systemic risk measures.