Effect of different basis functions on the LSM pricing of American option

Abstract:

American option allows an option holder to exercise the option at any time before the expiration of option. Thus it is impossible to price it by the B-S formula. Numerical methods are usually applied to price an American option. The least square Monte Carlo method (LSM) was firstly proposed by Longstaff and Schwartz in 2001, in which different basis functions in the least square regression can significantly affect the final pricing. In this study we discuss the effect of different basic functions on the American option pricing.

Key words:American option; LSM; Orthogonal polynomials; Basis function