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Sibuya copulas

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  • Marius Hofert
  • Frederic Vrins

Abstract

The standard intensity-based approach for modeling defaults is generalized by making the deterministic term structure of the survival probability stochastic via a common jump process. The survival copula of the vector of default times is derived and it is shown to be explicit and of the functional form as dealt with in the work of Sibuya. Besides the parameters of the jump process, the marginal survival functions of the default times appear in the copula. Sibuya copulas therefore allow for functional parameters and asymmetries. Due to the jump process in the construction, they allow for a singular component. Depending on the parameters, they may also be extreme-value copulas or Levy-frailty copulas. Further, Sibuya copulas are easy to sample in any dimension. Properties of Sibuya copulas including positive lower orthant dependence, tail dependence, and extremal dependence are investigated. An application to pricing first-to-default contracts is outlined and further generalizations of this copula class are addressed.

Suggested Citation

  • Marius Hofert & Frederic Vrins, 2010. "Sibuya copulas," Papers 1008.2292, arXiv.org.
    • Handle: RePEc:arx:papers:1008.2292
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    References listed on IDEAS

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    1. Hofert, Marius & Maechler, Martin, 2011. "Nested Archimedean Copulas Meet R: The nacopula Package," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 39(i09).
    2. Masaaki Sibuya, 1959. "Bivariate extreme statistics, I," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 11(2), pages 195-210, June.
    3. Frahm, Gabriel, 2006. "On the extremal dependence coefficient of multivariate distributions," Statistics & Probability Letters, Elsevier, vol. 76(14), pages 1470-1481, August.
    4. Lindqvist, Bo Henry, 1988. "Association of probability measures on partially ordered spaces," Journal of Multivariate Analysis, Elsevier, vol. 26(2), pages 111-132, August.
    5. McNeil, Alexander J. & Neslehová, Johanna, 2010. "From Archimedean to Liouville copulas," Journal of Multivariate Analysis, Elsevier, vol. 101(8), pages 1772-1790, September.
    6. Hofert, Marius & Mächler, Martin & McNeil, Alexander J., 2012. "Likelihood inference for Archimedean copulas in high dimensions under known margins," Journal of Multivariate Analysis, Elsevier, vol. 110(C), pages 133-150.
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    Cited by:

    1. Arbel, Julyan & Crispino, Marta & Girard, Stéphane, 2019. "Dependence properties and Bayesian inference for asymmetric multivariate copulas," Journal of Multivariate Analysis, Elsevier, vol. 174(C).
    2. Su, Jianxi & Hua, Lei, 2017. "A general approach to full-range tail dependence copulas," Insurance: Mathematics and Economics, Elsevier, vol. 77(C), pages 49-64.
    3. Philipp Arbenz & Mathieu Cambou & Marius Hofert, 2014. "An importance sampling approach for copula models in insurance," Papers 1403.4291, arXiv.org, revised Apr 2015.

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