Regression-Based Variance Reduction Approach for Strong Approximation Schemes

Abstract

In this paper, we present a novel approach towards variance reduction for discretised diffusion processes. The proposed approach involves specially constructed control variates and allows for a significant reduction in the variance for the terminal functionals. In this way, the complexity order of the standard Monte Carlo algorithm (ε-3) can be reduced down to ε-2|log(ε)| in case of the Euler scheme with ε being the precision to be achieved. These theoretical results are illustrated by several numerical examples.