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A Homotopy Analysis Method for the Option Pricing PDE in Post-Crash Markets

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  • El-Khatib Youssef

    (UAE University, Department of Mathematical Sciences, Al-Ain, P. O. Box 15551, United Arab Emirates)

Abstract

We investigate a solution for the option pricing partial differential equation (PDE) in a market suffering from a financial crisis. The post-crash model assumes that the volatility is stochastic. It is an extension of the famous Black and Scholes model. Therefore, the option pricing PDE for the crisis model is a generalization of the Black and Scholes PDE. However, to the best knowledge, it does not have a closed form solution for the general case. In this paper, we provide a solution for the pricing PDE of a European option during financial crisis using the homotopy analysis method.

Suggested Citation

  • El-Khatib Youssef, 2014. "A Homotopy Analysis Method for the Option Pricing PDE in Post-Crash Markets," Mathematical Economics Letters, De Gruyter, vol. 2(3-4), pages 45-50, November.
    • Handle: RePEc:bpj:maecol:v:2:y:2014:i:3-4:p:6:n:1
    DOI: 10.1515/mel-2013-0014
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    References listed on IDEAS

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    1. Robert Savit, 1989. "Nonlinearities and chaotic effects in options prices," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 9(6), pages 507-518, December.
    2. Savit, R., 1989. "Nonlinearities And Chaotic Effects In Options Prices," Papers 184, Columbia - Center for Futures Markets.
    3. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    4. Dibeh, Ghassan & Harmanani, Haidar M., 2007. "Option pricing during post-crash relaxation times," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 380(C), pages 357-365.
    5. Jostein Tvedt, 1998. "Valuation of a European futures option in the BIFFEX market," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 18(2), pages 167-175, April.
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