Abstract

The two popular systemic risk measures CoVaR (Conditional Value-at

Risk) and CoES (Conditional Expected Shortfall) have recently been receiving

growing attention on applications in economics and finance. In this paper, we

study the estimations of extreme CoVaR and CoES when the two random variables are asymptotic independent but positively associated.

We propose two

types of extrapolative approaches: the first relies on intermediate VaR and extrapolates it to extreme CoVaR/CoES via an adjustment factor; the second di-

rectly extrapolates the estimated intermediate CoVaR/CoES to the extreme tails.

All estimators, including both intermediate and extreme ones, are shown to be

asymptotically normal. Finally, we explore the empirical performances of our

methods through conducting a series of Monte Carlo simulations and a real data

analysis on S&P500 Index with 12 constituent stocks data.

Key words and phrases: Systemic risk measure; CoVaR; CoES; Asymptotic in- dependence

Information

Preprint No.SS-2026-0029
Manuscript IDSS-2026-0029
Complete AuthorsQingzhao Zhong
Corresponding AuthorsQingzhao Zhong
Emailsqzzhong22@m.fudan.edu.cn

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Acknowledgments

The author would like to thank the editor, associate editor, and two anonymous reviewers for their valuable comments and constructive suggestions,

which have helped improve the quality and presentation of this paper.

Supplementary Materials

The supplementary material contains all technical proofs, also provides additional simulations and empirical analyses.

Supplementary materials are available for download.