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A Simple Numerical Method for Pricing an American Put Option

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  • Beom Jin Kim
  • Yong-Ki Ma
  • Hi Jun Choe

Abstract

We present a simple numerical method to find the optimal exercise boundary in an American put option. We formulate an intermediate function with the fixed free boundary that has Lipschitz character near optimal exercise boundary. Employing it, we can easily determine the optimal exercise boundary by solving a quadratic equation in time‐recursive way. We also present several numerical results which illustrate a comparison to other methods.

Suggested Citation

  • Beom Jin Kim & Yong-Ki Ma & Hi Jun Choe, 2013. "A Simple Numerical Method for Pricing an American Put Option," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnljam:v:2013:y:2013:i:1:n:128025
    DOI: 10.1155/2013/128025
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    References listed on IDEAS

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    1. Jing Zhao & Hoi Ying Wong, 2012. "A closed-form solution to American options under general diffusion processes," Quantitative Finance, Taylor & Francis Journals, vol. 12(5), pages 725-737, July.
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    5. Robert C. Merton, 2005. "Theory of rational option pricing," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 8, pages 229-288, World Scientific Publishing Co. Pte. Ltd..
    6. Song-Ping Zhu, 2006. "An exact and explicit solution for the valuation of American put options," Quantitative Finance, Taylor & Francis Journals, vol. 6(3), pages 229-242.
    7. Geske, Robert & Johnson, Herb E, 1984. "The American Put Option Valued Analytically," Journal of Finance, American Finance Association, vol. 39(5), pages 1511-1524, December.
    8. Song-Ping Zhu, 2006. "A New Analytical Approximation Formula For The Optimal Exercise Boundary Of American Put Options," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 9(07), pages 1141-1177.
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    Cited by:

    1. Seung Hyun Kim, 2014. "Two Simple Numerical Methods for the Free Boundary in One‐Phase Stefan Problem," Journal of Applied Mathematics, John Wiley & Sons, vol. 2014(1).
    2. R. Company & V. N. Egorova & L. Jódar, 2014. "Solving American Option Pricing Models by the Front Fixing Method: Numerical Analysis and Computing," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).

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