Conditional risk measures in a bipartite market structure

TL;DR

This paper investigates how the network structure between agents and objects affects systemic risk measures in financial markets, using bipartite graphs and asymptotic analysis to quantify individual and collective risk contributions.

Contribution

It introduces a novel framework employing bipartite graphs and multivariate regular variation to analyze conditional systemic risk measures in large markets.

Findings

Asymptotic formulas for systemic risk measures based on Value-at-Risk and Conditional Tail Expectation.

Poisson approximations for constants in large insurance markets.

Detailed analysis and simulations of homogeneous random graph models.

Abstract

In this paper we study the effect of network structure between agents and objects on measures for systemic risk. We model the influence of sharing large exogeneous losses to the financial or (re)insuance market by a bipartite graph. Using Pareto-tailed losses and multivariate regular variation we obtain asymptotic results for systemic conditional risk measures based on the Value-at-Risk and the Conditional Tail Expectation. These results allow us to assess the influence of an individual institution on the systemic or market risk and vice versa through a collection of conditional systemic risk measures. For large markets Poisson approximations of the relevant constants are provided in the example of an insurance market. The example of an underlying homogeneous random graph is analysed in detail, and the results are illustrated through simulations.