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Lower Tail Dependence for Archimedean Copulas : Characterizations and Pitfalls

Author

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  • Charpentier, A.
  • Segers, J.J.J.

    (Tilburg University, Center For Economic Research)

Abstract

Tail dependence copulas provide a natural perspective from which one can study the dependence in the tail of a multivariate distribution.For Archimedean copulas with continuously differentiable generators, regular variation of the generator near the origin is known to be closely connected to convergence of the corresponding lower tail dependence copulas to the Clayton copula.In this paper, these characterizations are refined and extended to the case of generators which are not necessarily continuously differentiable.Moreover, a counterexample is constructed showing that even if the generator of a strict Archimedean copula is continuously differentiable and slowly varying at the origin, then the lower tail dependence copulas do not need to converge to the independent copula.
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Suggested Citation

  • Charpentier, A. & Segers, J.J.J., 2006. "Lower Tail Dependence for Archimedean Copulas : Characterizations and Pitfalls," Discussion Paper 2006-29, Tilburg University, Center for Economic Research.
    • Handle: RePEc:tiu:tiucen:ae669e5a-1929-42d9-b137-612af175d725
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    References listed on IDEAS

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    1. Arthur Charpentier & Alessandro Juri, 2004. "Limiting Dependence Structure for Credit Defaults," Working Papers 2004-16, Center for Research in Economics and Statistics.
    2. Klugman, Stuart A. & Parsa, Rahul, 1999. "Fitting bivariate loss distributions with copulas," Insurance: Mathematics and Economics, Elsevier, vol. 24(1-2), pages 139-148, March.
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    5. Charpentier, A. & Segers, J.J.J., 2006. "Convergence of Archimedean Copulas," Other publications TiSEM 410237d0-4c38-48f6-8f36-6, Tilburg University, School of Economics and Management.
    6. Bassan, Bruno & Spizzichino, Fabio, 2005. "Bivariate survival models with Clayton aging functions," Insurance: Mathematics and Economics, Elsevier, vol. 37(1), pages 6-12, August.
    7. Müller, Alfred & Scarsini, Marco, 2005. "Archimedean copulæ and positive dependence," Journal of Multivariate Analysis, Elsevier, vol. 93(2), pages 434-445, April.
    8. Edward Frees & Emiliano Valdez, 1998. "Understanding Relationships Using Copulas," North American Actuarial Journal, Taylor & Francis Journals, vol. 2(1), pages 1-25.
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    Citations

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    Cited by:

    1. Elena Di Bernardino & Didier Rullière, 2017. "A note on upper-patched generators for Archimedean copulas," Post-Print hal-01347869, HAL.
    2. Beare, Brendan K., 2012. "Archimedean Copulas And Temporal Dependence," Econometric Theory, Cambridge University Press, vol. 28(6), pages 1165-1185, December.
    3. repec:hal:wpaper:hal-00834000 is not listed on IDEAS
    4. Braekers, Roel & Van Keilegom, Ingrid, 2009. "Flexible modeling based on copulas in nonparametric median regression," Journal of Multivariate Analysis, Elsevier, vol. 100(6), pages 1270-1281, July.
    5. Di Bernardino Elena & Rullière Didier, 2013. "On certain transformations of Archimedean copulas: Application to the non-parametric estimation of their generators," Dependence Modeling, De Gruyter, vol. 1(2013), pages 1-36, October.
    6. Charpentier, Arthur & Segers, Johan, 2008. "Convergence of Archimedean copulas," Statistics & Probability Letters, Elsevier, vol. 78(4), pages 412-419, March.
    7. Di Bernardino, Elena & Maume-Deschamps, Véronique & Prieur, Clémentine, 2013. "Estimating a bivariate tail: A copula based approach," Journal of Multivariate Analysis, Elsevier, vol. 119(C), pages 81-100.
    8. Takaaki Koike & Marius Hofert, 2019. "Markov Chain Monte Carlo Methods for Estimating Systemic Risk Allocations," Papers 1909.11794, arXiv.org, revised May 2020.
    9. Hashorva, Enkelejd & Pakes, Anthony G. & Tang, Qihe, 2010. "Asymptotics of random contractions," Insurance: Mathematics and Economics, Elsevier, vol. 47(3), pages 405-414, December.
    10. Liebscher, Eckhard, 2008. "Construction of asymmetric multivariate copulas," Journal of Multivariate Analysis, Elsevier, vol. 99(10), pages 2234-2250, November.
    11. Hofert, Marius, 2021. "Right-truncated Archimedean and related copulas," Insurance: Mathematics and Economics, Elsevier, vol. 99(C), pages 79-91.
    12. Elena Di Bernardino & Didier Rullière, 2016. "On tail dependence coefficients of transformed multivariate Archimedean copulas," Post-Print hal-00992707, HAL.
    13. Constantinescu, Corina & Hashorva, Enkelejd & Ji, Lanpeng, 2011. "Archimedean copulas in finite and infinite dimensions—with application to ruin problems," Insurance: Mathematics and Economics, Elsevier, vol. 49(3), pages 487-495.
    14. Takaaki Koike & Marius Hofert, 2020. "Markov Chain Monte Carlo Methods for Estimating Systemic Risk Allocations," Risks, MDPI, vol. 8(1), pages 1-33, January.
    15. Yu, Lean & Zha, Rui & Stafylas, Dimitrios & He, Kaijian & Liu, Jia, 2020. "Dependences and volatility spillovers between the oil and stock markets: New evidence from the copula and VAR-BEKK-GARCH models," International Review of Financial Analysis, Elsevier, vol. 68(C).

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    More about this item

    Keywords

    Archimedean copula; regular variation; tail dependence; de Haan class;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General

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