Pricing American Options on Jump-Diffusion Processes using Fourier-Hermite Series Expansions
AbstractThis 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
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Bibliographic InfoPaper provided by Society for Computational Economics in its series Computing in Economics and Finance 2004 with number 177.
Date of creation: 11 Aug 2004
Date of revision:
American options; Fourier-Hermite series expansions; jump-diffusion;
Other versions of this item:
- Carl Chiarella & Andrew Ziogas, 2005. "Pricing American Options on Jump-Diffusion Processes using Fourier Hermite Series Expansions," Research Paper Series 145, Quantitative Finance Research Centre, University of Technology, Sydney.
- C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
- D11 - Microeconomics - - Household Behavior - - - Consumer Economics: Theory
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Amin, Kaushik I, 1993. " Jump Diffusion Option Valuation in Discrete Time," Journal of Finance, American Finance Association, vol. 48(5), pages 1833-63, December.
- Ball, Clifford A & Torous, Walter N, 1985. " On Jumps in Common Stock Prices and Their Impact on Call Option Pricing," Journal of Finance, American Finance Association, vol. 40(1), pages 155-73, March.
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