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Collocation Methods for Pricing American Strangle Options

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  • Jingtang Ma
  • Youjin Zhang

Abstract

The aim of this paper is to develop high-order collocation methods for pricing American strangle options. The major difficulty in pricing American strangles is to determine the optimal exercise boundaries. Chiarella and Ziogas (2005) derived that the optimal exercise boundaries satisfy a system of integral equations. Since the analytical solutions of the integral equation system cannot be found, it relies on numerical methods to solve the integral equation system. In the literature, there are no efficient and reliable numerical methods for solving the integral equation system. This paper develops a high-order collocation method to solve the integral equation system. Numerical example is carried out to show that the collocation methods are much more reliable and efficient.

Suggested Citation

  • Jingtang Ma & Youjin Zhang, 2012. "Collocation Methods for Pricing American Strangle Options," Accounting and Finance Research, Sciedu Press, vol. 1(1), pages 207-207, May.
    • Handle: RePEc:jfr:afr111:v:1:y:2012:i:1:p:207
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    References listed on IDEAS

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    1. Jing-Zhi Huang & Marti G. Subrahmanyam & G. George Yu, 1999. "Pricing And Hedging American Options: A Recursive Integration Method," World Scientific Book Chapters, in: Marco Avellaneda (ed.), Quantitative Analysis In Financial Markets Collected Papers of the New York University Mathematical Finance Seminar, chapter 8, pages 219-239, World Scientific Publishing Co. Pte. Ltd..
    2. Jérôme Detemple & Weidong Tian, 2002. "The Valuation of American Options for a Class of Diffusion Processes," Management Science, INFORMS, vol. 48(7), pages 917-937, July.
    3. G. Alobaidi & R. Mallier, 2002. "Laplace transforms and the American straddle," Journal of Applied Mathematics, Hindawi, vol. 2, pages 1-9, January.
    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.
    5. S. D. Jacka, 1991. "Optimal Stopping and the American Put," Mathematical Finance, Wiley Blackwell, vol. 1(2), pages 1-14, April.
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    JEL classification:

    • R00 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General - - - General
    • Z0 - Other Special Topics - - General

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