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Elliptical copulas: applicability and limitations

Author

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  • Frahm, Gabriel
  • Junker, Markus
  • Szimayer, Alexander

Abstract

We study copulas generated by elliptical distributions. We show that their tail dependence can be simply computed with default routines on Student's t-distribution given Kendall's [tau] and the tail index. The copula family generated by the sub-Gaussian [alpha]-stable distribution is unable to cover the size of tail dependence observed in financial data.

Suggested Citation

  • Frahm, Gabriel & Junker, Markus & Szimayer, Alexander, 2003. "Elliptical copulas: applicability and limitations," Statistics & Probability Letters, Elsevier, vol. 63(3), pages 275-286, July.
    • Handle: RePEc:eee:stapro:v:63:y:2003:i:3:p:275-286
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    References listed on IDEAS

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    1. Blattberg, Robert C & Gonedes, Nicholas J, 1974. "A Comparison of the Stable and Student Distributions as Statistical Models for Stock Prices," The Journal of Business, University of Chicago Press, vol. 47(2), pages 244-280, April.
    2. Sergio Ortobelli & Isabella Huber & Eduardo Schwartz, 2002. "Portfolio selection with stable distributed returns," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 55(2), pages 265-300, May.
    3. Rafael Schmidt, 2002. "Tail dependence for elliptically contoured distributions," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 55(2), pages 301-327, May.
    4. Fang, Hong-Bin & Fang, Kai-Tai & Kotz, Samuel, 2002. "The Meta-elliptical Distributions with Given Marginals," Journal of Multivariate Analysis, Elsevier, vol. 82(1), pages 1-16, July.
    5. Owen, Joel & Rabinovitch, Ramon, 1983. "On the Class of Elliptical Distributions and Their Applications to the Theory of Portfolio Choice," Journal of Finance, American Finance Association, vol. 38(3), pages 745-752, June.
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