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Paths and indices of maximal tail dependence

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  • Edward Furman
  • Jianxi Su
  • Riv{c}ardas Zitikis

Abstract

We demonstrate both analytically and numerically that the existing methods for measuring tail dependence in copulas may sometimes underestimate the extent of extreme co-movements of dependent risks and, therefore, may not always comply with the new paradigm of prudent risk management. This phenomenon holds in the context of both symmetric and asymmetric copulas with and without singularities. As a remedy, we introduce a notion of paths of maximal (tail) dependence and utilize it to propose several new indices of tail dependence. The suggested new indices are conservative, conform with the basic concepts of modern quantitative risk management, and are able to distinguish between distinct risky positions in situations when the existing indices fail to do so.

Suggested Citation

  • Edward Furman & Jianxi Su & Riv{c}ardas Zitikis, 2014. "Paths and indices of maximal tail dependence," Papers 1405.1326, arXiv.org, revised Jul 2016.
    • Handle: RePEc:arx:papers:1405.1326
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    References listed on IDEAS

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    1. Alexandra Ramos & Anthony Ledford, 2009. "A new class of models for bivariate joint tails," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(1), pages 219-241, January.
    2. 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.
    3. Fischer, Matthias J. & Klein, Ingo, 2007. "Some results on weak and strong tail dependence coefficients for means of copulas," Discussion Papers 78/2007, Friedrich-Alexander University Erlangen-Nuremberg, Chair of Statistics and Econometrics.
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    Cited by:

    1. Furman, Edward & Kuznetsov, Alexey & Su, Jianxi & Zitikis, Ričardas, 2016. "Tail dependence of the Gaussian copula revisited," Insurance: Mathematics and Economics, Elsevier, vol. 69(C), pages 97-103.

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