Regression-based variance reduction approach for strong approximation schemes

TL;DR

This paper introduces a new variance reduction method for discretized diffusion processes using control variates, significantly improving the efficiency of Monte Carlo simulations for terminal functionals.

Contribution

It proposes a novel variance reduction technique that reduces the complexity order of Monte Carlo algorithms from  to approximately , leveraging control variates for discretized diffusion processes.

Findings

Variance reduction significantly decreases simulation complexity.

Theoretical complexity bounds are validated by numerical examples.

Method improves efficiency of Monte Carlo for diffusion processes.

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 ($\varepsilon^{-3}$) can be reduced down to $\varepsilon^{-2}\sqrt{\left|\log(\varepsilon)\right|}$ in case of the Euler scheme with $\varepsilon$ being the precision to be achieved. These theoretical results are illustrated by several numerical examples.