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On a semi-spectral method for pricing an option on a mean-reverting asset

Author

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  • L. P. Bos
  • A. F. Ware
  • B. S. Pavlov

Abstract

We consider a risky asset following a mean-reverting stochastic process of the form [image omitted] We show that the (singular) diffusion equation which gives the value of a European option on S can be represented, upon expanding in Laguerre polynomials, by a tridiagonal infinite matrix. We analyse this matrix to show that the diffusion equation does indeed have a solution and truncate the matrix to give a simple, highly efficient method for the numerical calculation of the solution.

Suggested Citation

  • L. P. Bos & A. F. Ware & B. S. Pavlov, 2002. "On a semi-spectral method for pricing an option on a mean-reverting asset," Quantitative Finance, Taylor & Francis Journals, vol. 2(5), pages 337-345.
    • Handle: RePEc:taf:quantf:v:2:y:2002:i:5:p:337-345
    DOI: 10.1088/1469-7688/2/5/302
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    Cited by:

    1. Anatoliy Swishchuk, 2013. "Modeling and Pricing of Swaps for Financial and Energy Markets with Stochastic Volatilities," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 8660, December.
    2. Duy Nguyen & Jingzhi Tie & Qing Zhang, 2014. "An Optimal Trading Rule Under a Switchable Mean-Reversion Model," Journal of Optimization Theory and Applications, Springer, vol. 161(1), pages 145-163, April.

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