Extremal dependence of copulas: A tail density approach

Haijun Li and Peiling Wu

Journal of Multivariate Analysis, 2013, vol. 114, issue C, 99-111

Abstract: The extremal dependence of a random vector describes the tail behaviors of joint probabilities of the random vector with respect to that of its margins, and has been often studied by using the tail dependence function of its copula. A tail density approach is introduced in this paper to analyze extremal dependence of the copulas that are specified only by densities. The relation between the copula tail densities and regularly varying densities are established, and the tail densities of Archimedean and t copulas are derived explicitly. The tail density approach becomes especially effective for extremal dependence analysis on a vine copula, for which the tail density can be written recursively in the product form of tail densities of bivariate baseline copulas and densities of bivariate linking copulas.

Keywords: Tail dependence; Regularly varying density; Multivariate extremes; Tail risk; Vine copula (search for similar items in EconPapers)
Date: 2013
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Citations: View citations in EconPapers (9)

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DOI: 10.1016/j.jmva.2012.07.005

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