Quasi-Monte Carlo simulation for American option sensitivities

Abstract

The estimation of American option sensitivities is a challenging problem in financial engineering due to the stopping time involved. Progress has been made in using Monte Carlo (MC) simulation to obtain the estimation. However, the applicability of quasi-Monte Carlo (QMC) methods on estimating American option sensitivities is open. In this paper, we address this problem and propose efficient QMC methods for estimating American option sensitivities. Dimension reduction techniques, such as the Brownian bridge and principal component analysis, are used for further efficiency improvements. Numerical experiments in the cases of single underlying asset and multiple underlying assets under the Black–Scholes model and the variance gamma model demonstrate that QMC with dimension reduction techniques can significantly reduce the variance of the estimators of American option sensitivities.