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Efficient risk simulations for linear asset portfolios in the t-copula model

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  • Sak, Halis
  • Hörmann, Wolfgang
  • Leydold, Josef

Abstract

We consider the problem of calculating tail probabilities of the returns of linear asset portfolios. As a flexible and accurate model for the logarithmic returns we use the t-copula dependence structure and marginals following the generalized hyperbolic distribution. Exact calculation of the tail-loss probabilities is not possible and even simulation leads to challenging numerical problems. Applying a new numerical inversion method for the generation of the marginals and importance sampling with carefully selected mean shift we develop an efficient simulation algorithm. Numerical results for a variety of realistic portfolio examples show an impressive performance gain.

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  • 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.
  • Handle: RePEc:eee:ejores:v:202:y:2010:i:3:p:802-809
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    References listed on IDEAS

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    1. Paul Glasserman & Philip Heidelberger & Perwez Shahabuddin, 2002. "Portfolio Value‐at‐Risk with Heavy‐Tailed Risk Factors," Mathematical Finance, Wiley Blackwell, vol. 12(3), pages 239-269, July.
    2. Kole, Erik & Koedijk, Kees & Verbeek, Marno, 2007. "Selecting copulas for risk management," Journal of Banking & Finance, Elsevier, vol. 31(8), pages 2405-2423, August.
    3. Paul Glasserman & Philip Heidelberger & Perwez Shahabuddin, 1999. "Asymptotically Optimal Importance Sampling and Stratification for Pricing Path‐Dependent Options," Mathematical Finance, Wiley Blackwell, vol. 9(2), pages 117-152, April.
    4. Kjersti Aas & Ingrid Hobaek Haff, 2006. "The Generalized Hyperbolic Skew Student's t-Distribution," The Journal of Financial Econometrics, Society for Financial Econometrics, vol. 4(2), pages 275-309.
    5. 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.
    6. Andreas Behr & Ulrich Pötter, 2009. "Alternatives to the normal model of stock returns: Gaussian mixture, generalised logF and generalised hyperbolic models," Annals of Finance, Springer, vol. 5(1), pages 49-68, January.
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    Cited by:

    1. Erik Hintz & Marius Hofert & Christiane Lemieux & Yoshihiro Taniguchi, 2022. "Single-Index Importance Sampling with Stratification," Methodology and Computing in Applied Probability, Springer, vol. 24(4), pages 3049-3073, December.
    2. Plischke, Elmar & Borgonovo, Emanuele, 2019. "Copula theory and probabilistic sensitivity analysis: Is there a connection?," European Journal of Operational Research, Elsevier, vol. 277(3), pages 1046-1059.
    3. İsmail Başoğlu & Wolfgang Hörmann & Halis Sak, 2018. "Efficient simulations for a Bernoulli mixture model of portfolio credit risk," Annals of Operations Research, Springer, vol. 260(1), pages 113-128, January.
    4. Ruili Sun & Tiefeng Ma & Shuangzhe Liu & Milind Sathye, 2019. "Improved Covariance Matrix Estimation for Portfolio Risk Measurement: A Review," JRFM, MDPI, vol. 12(1), pages 1-34, March.
    5. Halis Sak & .Ismail Bac{s}ou{g}lu, 2015. "Efficient Randomized Quasi-Monte Carlo Methods For Portfolio Market Risk," Papers 1510.01593, arXiv.org.
    6. D’Amico, Guglielmo & Petroni, Filippo, 2018. "Copula based multivariate semi-Markov models with applications in high-frequency finance," European Journal of Operational Research, Elsevier, vol. 267(2), pages 765-777.
    7. Laih, Yih-Wenn, 2014. "Measuring rank correlation coefficients between financial time series: A GARCH-copula based sequence alignment algorithm," European Journal of Operational Research, Elsevier, vol. 232(2), pages 375-382.
    8. Sak, Halis & Başoğlu, İsmail, 2017. "Efficient randomized quasi-Monte Carlo methods for portfolio market risk," Insurance: Mathematics and Economics, Elsevier, vol. 76(C), pages 87-94.
    9. Sak Halis, 2010. "Increasing the number of inner replications of multifactor portfolio credit risk simulation in the t-copula model," Monte Carlo Methods and Applications, De Gruyter, vol. 16(3-4), pages 361-377, January.
    10. 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.
    11. Kemal Dinçer Dingeç & Wolfgang Hörmann, 2022. "Efficient Algorithms for Tail Probabilities of Exchangeable Lognormal Sums," Methodology and Computing in Applied Probability, Springer, vol. 24(3), pages 2093-2121, September.
    12. Hörmann, Wolfgang & Sak, Halis, 2010. "t-Copula generation for control variates," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 81(4), pages 782-790.

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