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

Author

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  • Andrew Ziogas
  • Carl Chiarella

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

Suggested Citation

  • Andrew Ziogas & Carl Chiarella, 2004. "Pricing American Options on Jump-Diffusion Processes using Fourier-Hermite Series Expansions," Computing in Economics and Finance 2004 177, Society for Computational Economics.
    • Handle: RePEc:sce:scecf4:177
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    3. Kein Joe Lau & Yong Kheng Goh & An Chow Lai, 2019. "An empirical study on asymmetric jump diffusion for option and annuity pricing," PLOS ONE, Public Library of Science, vol. 14(5), pages 1-18, May.
    4. Cosma, Antonio & Galluccio, Stefano & Pederzoli, Paola & Scaillet, Olivier, 2020. "Early Exercise Decision in American Options with Dividends, Stochastic Volatility, and Jumps," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 55(1), pages 331-356, February.
    5. Simon Scheidegger & Adrien Treccani, 2021. "Pricing American Options under High-Dimensional Models with Recursive Adaptive Sparse Expectations [Telling from Discrete Data Whether the Underlying Continuous-Time Model Is a Diffusion]," Journal of Financial Econometrics, Oxford University Press, vol. 19(2), pages 258-290.

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    More about this item

    Keywords

    American options; Fourier-Hermite series expansions; jump-diffusion;
    All these keywords.

    JEL classification:

    • 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

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