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High-order accurate implicit finite difference method for evaluating American options

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  • A. Mayo
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    Abstract

    A numerical method is presented for valuing vanilla American options on a single asset that is up to fourth-order accurate in the log of the asset price, and second-order accurate in time. The method overcomes the standard difficulty encountered in developing high-order accurate finite difference schemes for valuing American options; that is, the lack of smoothness in the option price at the critical boundary. This is done by making special corrections to the right-hand side of the differnce equations near the boundary, so they retain their level of accuracy. These corrections are easily evaluated using estimates of the boundary location and jump in the gamma that occurs there, such as those developed by Carr and Eaguet. Results of numerical experiments are presented comparing the method with more standard finite difference methods.

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    File URL: http://www.tandfonline.com/doi/abs/10.1080/1351847032000168641
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    Bibliographic Info

    Article provided by Taylor & Francis Journals in its journal The European Journal of Finance.

    Volume (Year): 10 (2004)
    Issue (Month): 3 ()
    Pages: 212-237

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    Handle: RePEc:taf:eurjfi:v:10:y:2004:i:3:p:212-237

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    Web page: http://www.tandfonline.com/REJF20

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    Related research

    Keywords: American options; finite difference method;

    References

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    1. 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 637-54, May-June.
    2. Zvan, R. & Vetzal, K. R. & Forsyth, P. A., 2000. "PDE methods for pricing barrier options," Journal of Economic Dynamics and Control, Elsevier, vol. 24(11-12), pages 1563-1590, October.
    3. Barone-Adesi, Giovanni & Whaley, Robert E, 1987. " Efficient Analytic Approximation of American Option Values," Journal of Finance, American Finance Association, vol. 42(2), pages 301-20, June.
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