T-Copula Generation For Control Variates - Hormann, Wolfgang; Sak, Halis (Elsevier Science Bv, Po Box 211, 1000 Ae Amsterdam, Netherlands, 2010)
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. (C) 2010 IMACS. Published by Elsevier B.V. All rights reserved.
Keywords: Monte Carlo simulation; t-Copula; Control variate; Polar method; risk; kontrol değişken; polar yöntem