Regression-based complexity reduction of the nested Monte Carlo methods

TL;DR

This paper introduces a dual regression-based method to simplify the nested Monte Carlo approach for pricing American options, especially effective for discretized diffusion processes, with analysis and numerical validation.

Contribution

It presents a novel regression-based technique that reduces computational complexity in nested Monte Carlo methods for American option pricing.

Findings

Significant reduction in computational complexity.

Effective for time discretized diffusion processes.

Validated through numerical examples.

Abstract

In this paper we propose a novel dual regression-based approach for pricing American options. This approach reduces the complexity of the nested Monte Carlo method and has especially simple form for time discretised diffusion processes. We analyse the complexity of the proposed approach both in the case of fixed and increasing number of exercise dates. The method is illustrated by several numerical examples.