JDOI Variance Reduction Method and the Pricing of American-Style Options

TL;DR

This paper extends the DOI variance reduction technique to efficiently price American-style options under jump-diffusion models, significantly reducing variance and speeding up Monte Carlo methods.

Contribution

It introduces the JDOI method, combining variance reduction with Monte Carlo algorithms for American options under Lévy processes, enhancing computational efficiency.

Findings

Strong variance reduction observed with JDOI method.

Improved speed of Monte Carlo-based pricing schemes.

Effective under general jump-diffusion stochastic volatility models.

Abstract

The present article revisits the Diffusion Operator Integral (DOI) variance reduction technique originally proposed in Heath and Platen (2002) and extends its theoretical concept to the pricing of American-style options under (time-homogeneous) L\'evy stochastic differential equations. The resulting Jump Diffusion Operator Integral (JDOI) method can be combined with numerous Monte Carlo based stopping-time algorithms, including the ubiquitous least-squares Monte Carlo (LSMC) algorithm of Longstaff and Schwartz (cf. Carriere (1996), Longstaff and Schwartz (2001)). We exemplify the usefulness of our theoretical derivations under a concrete, though very general jump-diffusion stochastic volatility dynamics and test the resulting LSMC based version of the JDOI method. The results provide evidence of a strong variance reduction when compared with a simple application of the LSMC algorithm and proves that applying our technique on top of Monte Carlo based pricing schemes provides a powerful way to speed-up these methods.