Efficient Risk Simulations for Linear Asset Portfolios in the t-Copula Model Halis Sak ∗,a , Wolfgang H¨ ormann b , Josef Leydold a a Department of Statistics and Mathematics, WU (Vienna University of Economics and Business), Augasse 2-6, A-1090 Wien, Austria b Department of Industrial Engineering, Bo˘ gazi¸ ci University, 34342 Bebek- ˙ Istanbul, Turkey 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 general- ized hyperbolic distribution. Exact calculation of the tail-loss probabilities is not possible and even simulation leads to challenging numerical problems. Apply- ing 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 exam- ples show an impressive performance gain. Key words: Risk management; importance sampling; linear asset portfolio; t-copula; generalized hyperbolic distribution 1. Introduction Estimation of the profit/loss distribution lies at the heart of risk management. However, computations of risk measures requires both the realistic modeling of * Corresponding Author: Department of Statistics and Mathematics, WU (Vienna University of Economics and Business), Augasse 2-6, A-1090 Wien, Austria. Phone: +43.1.31336-4180, Fax: +43.1.31336-774 Email addresses: halis.sak@wu.ac.at (Halis Sak), hormannw@boun.edu.tr (Wolfgang H¨ ormann), josef.leydold@wu.ac.at (Josef Leydold) Preprint submitted to Elsevier January 8, 2011