TY - JOUR

T1 - JDOI variance reduction method and the pricing of American-style options

AU - Auster, Johan

AU - Mathys, Ludovic

AU - Maeder, Fabio

PY - 2022

Y1 - 2022

N2 - This 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) Lévy 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) and 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.

AB - This 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) Lévy 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) and 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.

KW - Faculty of Science

KW - American options

KW - Lévy models

KW - Stochastic volatility

KW - Variance reduction

KW - Monte Carlo methods

U2 - 10.1080/14697688.2021.1962959

DO - 10.1080/14697688.2021.1962959

M3 - Journal article

VL - 22

SP - 639

EP - 656

JO - Quantitative Finance

JF - Quantitative Finance

SN - 1469-7688

IS - 4

ER -