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t-Copula generation for control variates

Author

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  • Hörmann, Wolfgang
  • Sak, Halis
Abstract
The standard method for generating multi-t vectors is simple and convenient but it has the disadvantage that the generated multi-normal and multi-t vectors are not similar. For t-copula models this destroys much of the variance reduction when using the result of the multi-normal model as external control variate. Therefore we develop a new generation method for multi-t vectors. It is based on the polar method and numerical inversion, and generates multi-normal and multi-t vectors that are very similar. Numerical experiments with simple functions of the weighted sum of t-copula vectors and with pricing European basket options with a t-copula model confirm that the obtained variance reduction factors of the new method are high; 2–100 times higher than when using the standard generation method.

Suggested Citation

  • Hörmann, Wolfgang & Sak, Halis, 2010. "t-Copula generation for control variates," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 81(4), pages 782-790.
    • Handle: RePEc:eee:matcom:v:81:y:2010:i:4:p:782-790
    DOI: 10.1016/j.matcom.2010.07.005
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    References listed on IDEAS

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    1. P. Pellizzari, 2001. "Efficient Monte Carlo pricing of European options¶using mean value control variates," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 24(2), pages 107-126, November.
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    4. Sak, Halis & Hörmann, Wolfgang & Leydold, Josef, 2010. "Efficient risk simulations for linear asset portfolios in the t-copula model," European Journal of Operational Research, Elsevier, vol. 202(3), pages 802-809, May.
    5. Kole, Erik & Koedijk, Kees & Verbeek, Marno, 2007. "Selecting copulas for risk management," Journal of Banking & Finance, Elsevier, vol. 31(8), pages 2405-2423, August.
    6. Achal Bassamboo & Sandeep Juneja & Assaf Zeevi, 2008. "Portfolio Credit Risk with Extremal Dependence: Asymptotic Analysis and Efficient Simulation," Operations Research, INFORMS, vol. 56(3), pages 593-606, June.
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    Cited by:

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    2. Stanislav Anatolyev & Vladimir Pyrlik, 2021. "Shrinkage for Gaussian and t Copulas in Ultra-High Dimensions," CERGE-EI Working Papers wp699, The Center for Economic Research and Graduate Education - Economics Institute, Prague.
    3. Ledermann, Daniel & Alexander, Carol, 2012. "Further properties of random orthogonal matrix simulation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 83(C), pages 56-79.
    4. Balaev, Alexey, 2014. "The copula based on multivariate t-distribution with vector of degrees of freedom," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 33(1), pages 90-110.

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