Pricing American Options on Jump-Diffusion Processes Using Fourier Hermite Series Expansions
Quantitative Finance Research Centre Research Paper No. 145
48 Pages Posted: 2 May 2006
Date Written: January 2005
Abstract
This paper presents a numerical method for pricing American call options where the underlying asset price follows a jump-diffusion process. The method is based on the Fourier-Hermite series expansions of Chiarella, El-Hassan & Kucera (1999), which we extend to allow for Poisson jumps, in the case where the jump sizes are log-normally distributed. The series approximation is applied to both European and American call options, and algorithms are presented for calculating the option price in each case. Since the series expansions only require discretisation in time to be implemented, the resulting price approximations require no asset price interpolation, and for certain maturities are demonstrated to produce both accurate and efficient solutions when compared with alternative methods, such as numerical integration, the method of lines and finite difference schemes.
Keywords: American options, jump-diffusion, Fourier-Hermite series expansions, free boundary problem
JEL Classification: C61, D11
Suggested Citation: Suggested Citation