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A sharp inequality for Kendall’s τ and Spearman’s ρ of Extreme-Value Copulas

Author

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  • Trutschnig Wolfgang

    (Department for Mathematics, University of Salzburg,Salzburg, Austria)

  • Mroz Thomas

    (Department for Mathematics, University of Salzburg,Salzburg, Austria)

Abstract

We derive a new (lower) inequality between Kendall’s τ and Spearman’s ρ for two-dimensional Extreme-Value Copulas, show that this inequality is sharp in each point and conclude that the comonotonic and the product copula are the only Extreme-Value Copulas for which the well-known lower Hutchinson-Lai inequality is sharp.

Suggested Citation

  • Trutschnig Wolfgang & Mroz Thomas, 2018. "A sharp inequality for Kendall’s τ and Spearman’s ρ of Extreme-Value Copulas," Dependence Modeling, De Gruyter, vol. 6(1), pages 369-376, December.
    • Handle: RePEc:vrs:demode:v:6:y:2018:i:1:p:369-376:n:21
    DOI: 10.1515/demo-2018-0021
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    References listed on IDEAS

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    1. Manuela Schreyer & Roland Paulin & Wolfgang Trutschnig, 2017. "On the exact region determined by Kendall's τ and Spearman's ρ," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 79(2), pages 613-633, March.
    2. François Longin & Bruno Solnik, 2001. "Extreme Correlation of International Equity Markets," Journal of Finance, American Finance Association, vol. 56(2), pages 649-676, April.
    3. Alexander J. McNeil & Rüdiger Frey & Paul Embrechts, 2015. "Quantitative Risk Management: Concepts, Techniques and Tools Revised edition," Economics Books, Princeton University Press, edition 2, number 10496.
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