Extreme Value Inference for CoVaR and Systemic Risk

TL;DR

This paper introduces an extreme value framework for CoVaR that links systemic risk measures to joint tail behaviors, enabling better risk assessment and management.

Contribution

It develops a new tail regime characterization for CoVaR, proposes a minimum-distance estimation method, and demonstrates practical systemic risk analysis applications.

Findings

The framework characterizes tail regimes via copula tail expansions.

The estimation approach accommodates multiple tail regimes.

Empirical analysis shows improved systemic risk assessment.

Abstract

We develop an extreme value framework for CoVaR centered on $v(q \mid p ; C)$, the copula-adjusted probability level, or equivalently, the CoVaR on the uniform (0,1) scale. We characterize the possible tail regimes of $v(q \mid p ; C)$ through the limit behavior of the copula conditional distribution and show that these regimes are determined by the joint tail expansions of the copula. This leads to tractable conditions for identifying the tail regime and deriving the asymptotic behavior of $v(q | p ; C)$. Building on this characterization, we propose a minimum-distance estimation approach for CoVaR that accommodates multiple tail regimes. The methodology links CoVaR and $\Delta$CoVaR to the underlying joint tail behavior, thereby providing a clear interpretation of these measures in systemic risk analysis. An empirical analysis across U.S. sectors demonstrates the practical value of the approach for assessing systemic risk contributions and exposures with important implications for macroprudential surveillance and risk management.