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Tail dependence of the Gaussian copula revisited

Author

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  • Furman, Edward
  • Kuznetsov, Alexey
  • Su, Jianxi
  • Zitikis, Ričardas

Abstract

Tail dependence refers to clustering of extreme events. In the context of financial risk management, the clustering of high-severity risks has a devastating effect on the well-being of firms and is thus of pivotal importance in risk analysis.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:insuma:v:69:y:2016:i:c:p:97-103
    DOI: 10.1016/j.insmatheco.2016.04.009
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    References listed on IDEAS

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    1. Joe, H., 1993. "Parametric Families of Multivariate Distributions with Given Margins," Journal of Multivariate Analysis, Elsevier, vol. 46(2), pages 262-282, August.
    2. Ruodu Wang & Liang Peng & Jingping Yang, 2013. "Bounds for the sum of dependent risks and worst Value-at-Risk with monotone marginal densities," Finance and Stochastics, Springer, vol. 17(2), pages 395-417, April.
    3. Joe, Harry & Li, Haijun & Nikoloulopoulos, Aristidis K., 2010. "Tail dependence functions and vine copulas," Journal of Multivariate Analysis, Elsevier, vol. 101(1), pages 252-270, January.
    4. John R. Graham & Campbell R. Harvey, 2001. "Expectations of Equity Risk Premia, Volatility and Asymmetry from a Corporate Finance Perspective," NBER Working Papers 8678, National Bureau of Economic Research, Inc.
    5. 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.
    6. Donnelly, Catherine & Embrechts, Paul, 2010. "The Devil is in the Tails: Actuarial Mathematics and the Subprime Mortgage Crisis," ASTIN Bulletin, Cambridge University Press, vol. 40(1), pages 1-33, May.
    7. Furman, Edward & Su, Jianxi & Zitikis, RiÄ ardas, 2015. "Paths And Indices Of Maximal Tail Dependence," ASTIN Bulletin, Cambridge University Press, vol. 45(3), pages 661-678, September.
    8. 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.
    9. Zhang, Ming-Heng, 2008. "Modelling total tail dependence along diagonals," Insurance: Mathematics and Economics, Elsevier, vol. 42(1), pages 73-80, February.
    10. Kousky, Carolyn & Cooke, Roger M., 2009. "The Unholy Trinity: Fat Tails, Tail Dependence, and Micro-Correlations," RFF Working Paper Series dp-09-36-rev.pdf, Resources for the Future.
    11. Hua, Lei & Joe, Harry, 2014. "Strength of tail dependence based on conditional tail expectation," Journal of Multivariate Analysis, Elsevier, vol. 123(C), pages 143-159.
    12. Asimit, Alexandru V. & Gerrard, Russell & Hou, Yanxi & Peng, Liang, 2016. "Tail dependence measure for examining financial extreme co-movements," Journal of Econometrics, Elsevier, vol. 194(2), pages 330-348.
    13. Fung, Thomas & Seneta, Eugene, 2011. "The bivariate normal copula function is regularly varying," Statistics & Probability Letters, Elsevier, vol. 81(11), pages 1670-1676, November.
    14. Edward Furman & Jianxi Su & Riv{c}ardas Zitikis, 2014. "Paths and indices of maximal tail dependence," Papers 1405.1326, arXiv.org, revised Jul 2016.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Bikramjit Das & Vicky Fasen-Hartmann, 2023. "Aggregating heavy-tailed random vectors: from finite sums to L\'evy processes," Papers 2301.10423, arXiv.org.
    2. Xin Liu & Jiang Wu & Chen Yang & Wenjun Jiang, 2018. "A Maximal Tail Dependence-Based Clustering Procedure for Financial Time Series and Its Applications in Portfolio Selection," Risks, MDPI, vol. 6(4), pages 1-26, October.
    3. Indranil Ghosh & Filipe J. Marques, 2021. "Tail Conditional Expectations Based on Kumaraswamy Dispersion Models," Mathematics, MDPI, vol. 9(13), pages 1-17, June.
    4. Bikramjit Das & Vicky Fasen-Hartmann, 2023. "Systemic risk in financial networks: the effects of asymptotic independence," Papers 2309.15511, arXiv.org.
    5. J. C. Arismendi-Zambrano & Vladimir Belitsky & Vinicius Amorim Sobreiro & Herbert Kimura, 2020. "The Implications of Tail Dependency Measures for Counterparty Credit Risk Pricing," Economics Department Working Paper Series n306-20.pdf, Department of Economics, National University of Ireland - Maynooth.
    6. Jianxi Su & Edward Furman, 2016. "Multiple risk factor dependence structures: Copulas and related properties," Papers 1610.02126, arXiv.org.
    7. Federico Pasquale Cortese, 2019. "Tail Dependence in Financial Markets: A Dynamic Copula Approach," Risks, MDPI, vol. 7(4), pages 1-14, November.
    8. Bikramjit Das & Vicky Fasen-Hartmann, 2023. "On heavy-tailed risks under Gaussian copula: the effects of marginal transformation," Papers 2304.05004, arXiv.org.
    9. Su, Jianxi & Furman, Edward, 2017. "Multiple risk factor dependence structures: Copulas and related properties," Insurance: Mathematics and Economics, Elsevier, vol. 74(C), pages 109-121.
    10. Arismendi-Zambrano, Juan & Belitsky, Vladimir & Sobreiro, Vinicius Amorim & Kimura, Herbert, 2022. "The implications of dependence, tail dependence, and bounds’ measures for counterparty credit risk pricing," Journal of Financial Stability, Elsevier, vol. 58(C).

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    More about this item

    Keywords

    Diagonal; Gaussian copula; Maximal tail dependence; Tail independence; Index of tail dependence;
    All these keywords.

    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation

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