Measuring risk contagion in financial networks with CoVaR

TL;DR

This paper introduces a new framework for measuring risk contagion in financial networks using CoVaR and the Extreme CoVaR Index, accounting for heavy-tailed asset returns and various dependence structures.

Contribution

It develops asymptotic analysis of CoVaR and proposes the Extreme CoVaR Index for better risk contagion measurement in complex financial networks.

Findings

Derived explicit formulas for CoVaR under Gaussian and Marshall-Olkin copulas.

Introduced the Extreme CoVaR Index for networks with asymptotic independence.

Analyzed the impact of different dependence structures on risk contagion measures.

Abstract

The stability of a complex financial system may be assessed by measuring risk contagion between various financial institutions with relatively high exposure. We consider a financial network model using a bipartite graph of financial institutions (e.g., banks, investment companies, insurance firms) on one side and financial assets on the other. Following empirical evidence, returns from such risky assets are modeled by heavy-tailed distributions, whereas their joint dependence is characterized by copula models exhibiting a variety of tail dependence behavior. We consider CoVaR, a popular measure of risk contagion and study its asymptotic behavior under broad model assumptions. We further propose the Extreme CoVaR Index (ECI) for capturing the strength of risk contagion between risk entities in such networks, which is particularly useful for models exhibiting asymptotic independence. The results are illustrated by providing precise expressions of CoVaR and ECI when the dependence of the assets is modeled using two well-known multivariate dependence structures: the Gaussian copula and the Marshall-Olkin copula.