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Properties of CoVaR based on tail expansions of copulas

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  • Li, Xiaoting
  • Joe, Harry

Abstract

The theoretical properties of two widely used CoVaR definitions are investigated under different dependence structures in joint distributions. By using copulas, the dependence is separated from marginal distributions, and CoVaR is expressed through an adjustment factor based solely on the copula. The primary contribution is to study the limiting behavior of the adjustment factor and its link to the strength of dependence in the tails of the joint distribution. We also provide asymptotic results for bivariate Archimedean copulas and extend these findings to extreme value copulas and their mixtures. These findings enhance the understanding of CoVaR in risk scenarios, particularly as the conditional event becomes more extreme.

Suggested Citation

  • Li, Xiaoting & Joe, Harry, 2026. "Properties of CoVaR based on tail expansions of copulas," Journal of Multivariate Analysis, Elsevier, vol. 211(C).
    • Handle: RePEc:eee:jmvana:v:211:y:2026:i:c:s0047259x25001058
    DOI: 10.1016/j.jmva.2025.105510
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    References listed on IDEAS

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    1. Einmahl, J.H.J. & Krajina, A. & Segers, J., 2011. "An M-Estimator for Tail Dependence in Arbitrary Dimensions," Discussion Paper 2011-013, Tilburg University, Center for Economic Research.
    2. Li, Xiaoting & Joe, Harry, 2023. "Estimation of multivariate tail quantities," Computational Statistics & Data Analysis, Elsevier, vol. 185(C).
    3. Joe, Harry & Ma, Chunsheng, 2000. "Multivariate Survival Functions with a Min-Stable Property," Journal of Multivariate Analysis, Elsevier, vol. 75(1), pages 13-35, October.
    4. Girardi, Giulio & Tolga Ergün, A., 2013. "Systemic risk measurement: Multivariate GARCH estimation of CoVaR," Journal of Banking & Finance, Elsevier, vol. 37(8), pages 3169-3180.
    5. Capéraà, Philippe & Fougères, Anne-Laure & Genest, Christian, 2000. "Bivariate Distributions with Given Extreme Value Attractor," Journal of Multivariate Analysis, Elsevier, vol. 72(1), pages 30-49, January.
    6. Joe, Harry & Li, Haijun & Nikoloulopoulos, Aristidis K., 2010. "Tail dependence functions and vine copulas," Journal of Multivariate Analysis, Elsevier, vol. 101(1), pages 252-270, January.
    7. Bernardi, M. & Durante, F. & Jaworski, P., 2017. "CoVaR of families of copulas," Statistics & Probability Letters, Elsevier, vol. 120(C), pages 8-17.
    8. Joe, Harry & Hu, Taizhong, 1996. "Multivariate Distributions from Mixtures of Max-Infinitely Divisible Distributions," Journal of Multivariate Analysis, Elsevier, vol. 57(2), pages 240-265, May.
    9. Piotr Jaworski, 2017. "On the Conditional Value-at-Risk (CoVaR) in copula setting," Springer Books, in: Manuel Úbeda Flores & Enrique de Amo Artero & Fabrizio Durante & Juan Fernández Sánchez (ed.), Copulas and Dependence Models with Applications, chapter 0, pages 95-117, Springer.
    10. Hua, Lei & Joe, Harry, 2011. "Tail order and intermediate tail dependence of multivariate copulas," Journal of Multivariate Analysis, Elsevier, vol. 102(10), pages 1454-1471, November.
    Full references (including those not matched with items on IDEAS)

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