Polar generation of random variates with the t-distribution
Mathematics of Computation
Accurate closed-form approximation for pricing Asian and basket options
Applied Stochastic Models in Business and Industry
Random variate generation by numerical inversion when only the density is known
ACM Transactions on Modeling and Computer Simulation (TOMACS)
Original article: Further properties of random orthogonal matrix simulation
Mathematics and Computers in Simulation
Identifying the attribute of joint demand in Chinese payment card market
International Journal of Electronic Finance
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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.