Extreme Value Inference for CoVaR and Systemic Risk

2026-03-28

AI Summary

This study addresses the challenge of measuring systemic risk under extreme market stress by proposing a conditional Value-at-Risk (CoVaR) framework grounded in extreme value theory. By characterizing the limiting behavior of copula-based conditional distributions in joint tail regions, the work establishes, for the first time, an explicit link between CoVaR and the copula’s joint tail structure. It identifies the asymptotic properties of CoVaR under various tail dependence scenarios and develops a unified minimum distance estimation method applicable across diverse tail structures. Empirical analysis demonstrates that the proposed approach effectively uncovers heterogeneous contributions to and exposures from systemic risk across U.S. industries, offering macroprudential regulators and risk managers an interpretable and robust analytical tool.

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 $Δ$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.

Problem

• CoVaR
• Extreme Value
• Systemic Risk
• Copula
• Tail Dependence

Innovation

• Extreme Value Theory
• CoVaR
• Copula
• Tail Dependence
• Systemic Risk