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Dependence structure of conditional Archimedean copulas

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  • Mesfioui, Mhamed
  • Quessy, Jean-François

Abstract

In this article, copulas associated to multivariate conditional distributions in an Archimedean model are characterized. It is shown that this popular class of dependence structures is closed under the operation of conditioning, but that the associated conditional copula has a different analytical form in general. It is also demonstrated that the extremal copula for conditional Archimedean distributions is no longer the Frechet upper bound, but rather a member of the Clayton family. Properties of these conditional distributions as well as conditional versions of tail dependence indices are also considered.

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  • Mesfioui, Mhamed & Quessy, Jean-François, 2008. "Dependence structure of conditional Archimedean copulas," Journal of Multivariate Analysis, Elsevier, vol. 99(3), pages 372-385, March.
    • Handle: RePEc:eee:jmvana:v:99:y:2008:i:3:p:372-385
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    3. Brechmann, Eike C. & Hendrich, Katharina & Czado, Claudia, 2013. "Conditional copula simulation for systemic risk stress testing," Insurance: Mathematics and Economics, Elsevier, vol. 53(3), pages 722-732.
    4. Philipp Arbenz & Mathieu Cambou & Marius Hofert, 2014. "An importance sampling approach for copula models in insurance," Papers 1403.4291, arXiv.org, revised Apr 2015.
    5. Gijbels Irène & Matterne Margot, 2021. "Study of partial and average conditional Kendall’s tau," Dependence Modeling, De Gruyter, vol. 9(1), pages 82-120, January.
    6. Huynh, Toan Luu Duc & Nasir, Muhammad Ali & Nguyen, Sang Phu & Duong, Duy, 2020. "An assessment of contagion risks in the banking system using non-parametric and Copula approaches," Economic Analysis and Policy, Elsevier, vol. 65(C), pages 105-116.
    7. Grothe, Oliver & Hofert, Marius, 2015. "Construction and sampling of Archimedean and nested Archimedean Lévy copulas," Journal of Multivariate Analysis, Elsevier, vol. 138(C), pages 182-198.
    8. Spanhel, Fabian & Kurz, Malte S., 2016. "The partial copula: Properties and associated dependence measures," Statistics & Probability Letters, Elsevier, vol. 119(C), pages 76-83.
    9. Stöber, Jakob & Joe, Harry & Czado, Claudia, 2013. "Simplified pair copula constructions—Limitations and extensions," Journal of Multivariate Analysis, Elsevier, vol. 119(C), pages 101-118.
    10. Atskanov, Isuf, 2015. "Dynamic optimization of an investment portfolio on European stock markets using pair copulas," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 40(4), pages 84-105.

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