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

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  • A. Mayo

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.

Suggested Citation

  • A. Mayo, 2004. "High-order accurate implicit finite difference method for evaluating American options," The European Journal of Finance, Taylor & Francis Journals, vol. 10(3), pages 212-237.
    • Handle: RePEc:taf:eurjfi:v:10:y:2004:i:3:p:212-237
    DOI: 10.1080/1351847032000168641
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    References listed on IDEAS

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    1. Carr, Peter, 1998. "Randomization and the American Put," The Review of Financial Studies, Society for Financial Studies, vol. 11(3), pages 597-626.
    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 301-320, June.
    4. 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.
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    Cited by:

    1. Chinonso Nwankwo & Weizhong Dai, 2020. "Explicit RKF-Compact Scheme for Pricing Regime Switching American Options with Varying Time Step," Papers 2012.09820, arXiv.org, revised Feb 2022.
    2. JC Ndogmo, 2008. "Some Control Variates for exotic options," Papers 0806.4675, arXiv.org.
    3. Deng, Dingwen & Liang, Dong, 2018. "The time fourth-order compact ADI methods for solving two-dimensional nonlinear wave equations," Applied Mathematics and Computation, Elsevier, vol. 329(C), pages 188-209.
    4. J. C. Ndogmo & D. B. Ntwiga, 2007. "High-order accurate implicit methods for the pricing of barrier options," Papers 0710.0069, arXiv.org.

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    Keywords

    American options; finite difference method;

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