Acceleration of quasi-Monte Carlo approximations with applications in mathematical finance

Abstract

A procedure to accelerate the convergence of quasi-Monte Carlo approximations is described and investigated. The procedure applies a weighted least-squares smoothing method to improve the approximations that were obtained using low-discrepancy sequences. The acceleration procedure is tested computationally on several numerical integration problems including two problems of interest in mathematical finance. The results indicate that when Halton low-discrepancy points are used in the quasi-Monte Carlo method, the accelerated sequence often converges a factor of five or more faster than the original quasi-Monte Carlo approximations.