Efficient simulation of the price and the sensitivities of basket options under time-changed Brownian motions

We propose a new variance reduction method for the price and the sensitivities of basket options under time-changed Brownian motion models. The new algorithm combines the pathwise derivative method with control variates, conditional Monte Carlo, and randomized quasi?Monte Carlo. Control variates are constructed by using the conditioning variables of lower bounds of basket options for the purpose of variance reduction. Conditional Monte Carlo further reduces the variance by integrating out the selected conditioning variable. The smoothing effect of conditional Monte Carlo enhances the pathwise derivative and the randomized quasi?Monte Carlo methods. Computational experiments show that the new algorithm yields significant variance reductions.