Systemic Risk Models for Disjoint and Overlapping Groups with Equilibrium Strategies

TL;DR

This paper develops new systemic risk models for disjoint and overlapping groups, incorporating strategic choice and equilibrium analysis, with explicit solutions and numerical algorithms validated on real data.

Contribution

It introduces a generalized systemic risk measure allowing banks to choose groups, and provides equilibrium analysis, explicit risk allocations, and numerical methods validated with real data.

Findings

Explicit equilibrium solutions under Gaussian risk assumptions

Numerical algorithms for simulating systemic risk scenarios

Validation of models using real bank-CCP data

Abstract

We analyze the systemic risk for disjoint and overlapping groups (e.g., central clearing counterparties (CCP)) by proposing new models with realistic game features. Specifically, we generalize the systemic risk measure proposed in [F. Biagini, J.-P. Fouque, M. Frittelli, and T. Meyer-Brandis, Finance and Stochastics, 24(2020), 513--564] by allowing individual banks to choose their preferred groups instead of being assigned to certain groups. We introduce the concept of Nash equilibrium for these new models, and analyze the optimal solution under Gaussian distribution of the risk factor. We also provide an explicit solution for the risk allocation of the individual banks, and study the existence and uniqueness of Nash equilibrium both theoretically and numerically. The developed numerical algorithm can simulate scenarios of equilibrium, and we apply it to study the bank-CCP structure with real data and show the validity of the proposed model.