Randomized quasi-Monte Carlo: a tool for improving the efficiency of simulations in finance

Quasi-Monte Carlo (QMC) methods have been used in a variety of problems in finance over the last few years, where they often provide more accurate estimators than the Monte Carlo (MC) method. These results have led many researchers to try to find reasons for the success of QMC methods in finance. A general explanation is that financial problems often have a structure that interacts in a constructive way with the point set used by the QMC method, thus resulting in estimators with reduced error. This positive interaction can be amplified by various fine-tuning techniques, which we review in the first part of this paper. Leaving aside these techniques, we then choose a few randomized QMC methods and test their "robustness" by comparing their performance against MC on different financial problems. Our results suggest that the chosen methods are efficient in a broad sense for financial simulations.