Accelerated variance reduction methods on GPU

Monte Carlo simulations have become widely used in computational finance. Standard error is the basic notion to measure the quality of a Monte Carlo estimator, and the square of standard error is defined as the variance divided by the total number of simulations. Variance reduction methods have been developed as efficient algorithms by means of probabilistic analysis. GPU acceleration plays a crucial role of increasing the total number of simulations. We show that the total effect of combining variance reduction methods as efficient software algorithms with GPU acceleration as a parallel-computing hardware device can yield a tremendous speed up for financial applications such as evaluation of option prices and estimation of joint default probabilities.