Efficient Risk Simulations for Linear Asset Portfolios

We consider the problem of calculating tail probabilities of the returns of linear asset portfolios. As 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.