Pricing American Options on Jump-Diffusion Processes using Fourier-Hermite Series Expansions

Andrew Ziogas and Carl Chiarella

No 177, Computing in Economics and Finance 2004 from Society for Computational Economics

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 and 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 are demonstrated to produce both accurate and efficient solutions when compared with alternative methods, such as numerical integration and the method of lines

Keywords: American options; Fourier-Hermite series expansions; jump-diffusion (search for similar items in EconPapers)
JEL-codes: C61 D11 (search for similar items in EconPapers)
Date: 2004-08-11
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Working Paper: Pricing American Options on Jump-Diffusion Processes using Fourier Hermite Series Expansions (2005)
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