Improved Monte Carlo and quasi-Monte Carlo methods for the price and the Greeks of Asian options

An improved variance reduction method for accurate estimation of the price, delta, and gamma of Asian options in a single simulation is presented. It combines randomized quasi-Monte Carlo with very efficient new control variates, that are especially successful in reducing the variance of the pathwise derivative method used to simulate delta and gamma. To improve the performance of randomized quasi-Monte Carlo, we smooth the integrands by employing conditional Monte Carlo and reduce the effective dimension of the smoothed integrands by using principal component analysis. Numerical results show that the new method yields significant variance reduction for the price, for delta and for gamma.