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The t copula with Multiple Parameters of Degrees of Freedom: Bivariate Characteristics and Application to Risk Management

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  • Xiaolin Luo
  • Pavel V. Shevchenko

Abstract

The t copula is often used in risk management as it allows for modelling tail dependence between risks and it is simple to simulate and calibrate. However, the use of a standard t copula is often criticized due to its restriction of having a single parameter for the degrees of freedom (dof) that may limit its capability to model the tail dependence structure in a multivariate case. To overcome this problem, grouped t copula was proposed recently, where risks are grouped a priori in such a way that each group has a standard t copula with its specific dof parameter. In this paper we propose the use of a grouped t copula, where each group consists of one risk factor only, so that a priori grouping is not required. The copula characteristics in the bivariate case are studied. We explain simulation and calibration procedures, including a simulation study on finite sample properties of the maximum likelihood estimators and Kendall's tau approximation. This new copula can be significantly different from the standard t copula in terms of risk measures such as tail dependence, value at risk and expected shortfall. Keywords: grouped t copula, tail dependence, risk management.

Suggested Citation

  • Xiaolin Luo & Pavel V. Shevchenko, 2007. "The t copula with Multiple Parameters of Degrees of Freedom: Bivariate Characteristics and Application to Risk Management," Papers 0710.3959, arXiv.org, revised Feb 2010.
    • Handle: RePEc:arx:papers:0710.3959
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    References listed on IDEAS

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    1. 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.
    2. 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.
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    Cited by:

    1. Cordelia Rudolph & Uwe Schmock, 2020. "Multivariate Collective Risk Model: Dependent Claim Numbers and Panjer’s Recursion," Risks, MDPI, vol. 8(2), pages 1-31, May.
    2. Penikas, Henry, 2014. "Investment portfolio risk modelling based on hierarchical copulas," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 35(3), pages 18-38.
    3. Fuchs, Sebastian & Tschimpke, Marco, 2024. "A novel positive dependence property and its impact on a popular class of concordance measures," Journal of Multivariate Analysis, Elsevier, vol. 200(C).
    4. Hua, Lei & Joe, Harry, 2017. "Multivariate dependence modeling based on comonotonic factors," Journal of Multivariate Analysis, Elsevier, vol. 155(C), pages 317-333.
    5. Brechmann, Eike & Czado, Claudia & Paterlini, Sandra, 2014. "Flexible dependence modeling of operational risk losses and its impact on total capital requirements," Journal of Banking & Finance, Elsevier, vol. 40(C), pages 271-285.
    6. Fermanian, Jean-David & Wegkamp, Marten H., 2012. "Time-dependent copulas," Journal of Multivariate Analysis, Elsevier, vol. 110(C), pages 19-29.

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