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.

Truncated control variates for weak approximation schemes

“…For the TRCV approach with the second order weak schemes under (B1)-(B5), it is optimal to choose the orders of parameters as follows (cf. [4]) 3 Notice that the variance of the TRCV estimate 1 provided that κ > 1. 4 Thus, we have for the complexity…”