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The bivariate normal copula function is regularly varying

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  • Fung, Thomas
  • Seneta, Eugene

Abstract

We derive the rate of decay of the tail dependence of the bivariate normal distribution and establish its link with regularly varying functions. This result is an initial step in explaining the discrepancy between a zero asymptotic tail dependence coefficient and mass in the tail of a joint distribution.

Suggested Citation

  • Fung, Thomas & Seneta, Eugene, 2011. "The bivariate normal copula function is regularly varying," Statistics & Probability Letters, Elsevier, vol. 81(11), pages 1670-1676, November.
    • Handle: RePEc:eee:stapro:v:81:y:2011:i:11:p:1670-1676
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    References listed on IDEAS

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    1. Elisa Luciano & Wim Schoutens, 2006. "A multivariate jump-driven financial asset model," Quantitative Finance, Taylor & Francis Journals, vol. 6(5), pages 385-402.
    2. Thomas Fung & Eugene Seneta, 2010. "Modelling and Estimation for Bivariate Financial Returns," International Statistical Review, International Statistical Institute, vol. 78(1), pages 117-133, April.
    3. Schmid, Friedrich & Schmidt, Rafael, 2007. "Multivariate conditional versions of Spearman's rho and related measures of tail dependence," Journal of Multivariate Analysis, Elsevier, vol. 98(6), pages 1123-1140, July.
    4. Fung, Thomas & Seneta, Eugene, 2010. "Tail dependence for two skew t distributions," Statistics & Probability Letters, Elsevier, vol. 80(9-10), pages 784-791, May.
    5. Banachewicz, Konrad & van der Vaart, Aad, 2008. "Tail dependence of skewed grouped t-distributions," Statistics & Probability Letters, Elsevier, vol. 78(15), pages 2388-2399, October.
    6. Thomas Fung & Eugene Seneta, 2010. "Tail dependence and skew distributions," Quantitative Finance, Taylor & Francis Journals, vol. 11(3), pages 327-333.
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    Cited by:

    1. Hu, Shuang & Peng, Zuoxiang & Nadarajah, Saralees, 2022. "Tail dependence functions of the bivariate Hüsler–Reiss model," Statistics & Probability Letters, Elsevier, vol. 180(C).
    2. Fung, Thomas & Seneta, Eugene, 2016. "Tail asymptotics for the bivariate skew normal," Journal of Multivariate Analysis, Elsevier, vol. 144(C), pages 129-138.
    3. Xin Lao & Zuoxiang Peng & Saralees Nadarajah, 2023. "Tail Dependence Functions of Two Classes of Bivariate Skew Distributions," Methodology and Computing in Applied Probability, Springer, vol. 25(1), pages 1-24, March.
    4. 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.
    5. Thomas Fung & Eugene Seneta, 2018. "Quantile Function Expansion Using Regularly Varying Functions," Methodology and Computing in Applied Probability, Springer, vol. 20(4), pages 1091-1103, December.
    6. Fung, Thomas & Seneta, Eugene, 2014. "Convergence rate to a lower tail dependence coefficient of a skew-t distribution," Journal of Multivariate Analysis, Elsevier, vol. 128(C), pages 62-72.

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