t-Copula generation for control variates

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.