Variance reduction for discretised diffusions via regression

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 (epsilon(-3) in the case of a first order scheme and epsilon(-2.5) in the case of a second order scheme) can be reduced down to epsilon(-2+delta) for any delta is an element of [0, 0.25) with epsilon being the precision to be achieved. These theoretical results are illustrated by several numerical examples. (C) 2017 Elsevier Inc. All rights reserved.