Combining Latin hypercube sampling with other variance reduction techniques

We consider the problem of reducing the variance of Monte Carlo estimators of high-dimensional estimation problems by combining the variance reduction techniques Latin hypercube sampling with dependence (LHSD), control variates and importance sampling. Under some standard conditions, the resulting estimators are consistent and asymptotically unbiased, and a central limit theorem holds. The effectiveness of the combined variance reduction methods is investigated by pricing an Asian basket call option. When comparing the effectiveness with existing combined variance reduction techniques, it turns out that techniques highly tailored to the specific problem are more effective, but among the methods that make no use of specific information, LHSD performs best. Since LHSD is easy to apply, our results indicate that it is worthwhile to test the performance pickup of integrating LHSD into arbitrary simulation problems even when a variance reduction technique is already in place.