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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, Hindawi, vol. 2013, pages 1-7, February.
    • Handle: RePEc:hin:jnljam:128025
    DOI: 10.1155/2013/128025
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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. Lee, Jung-Kyung, 2020. "A simple numerical method for pricing American power put options," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    3. D. Belomestny & M. Kaledin & J. Schoenmakers, 2019. "Semi-tractability of optimal stopping problems via a weighted stochastic mesh algorithm," Papers 1906.09431, arXiv.org.
    4. Jung-Kyung Lee, 2020. "On a Free Boundary Problem for American Options Under the Generalized Black–Scholes Model," Mathematics, MDPI, vol. 8(9), pages 1-11, September.
    5. Chinonso Nwankwo & Weizhong Dai, 2020. "An Adaptive and Explicit Fourth Order Runge-Kutta-Fehlberg Method Coupled with Compact Finite Differencing for Pricing American Put Options," Papers 2007.04408, arXiv.org, revised Jul 2021.
    6. Denis Belomestny & Maxim Kaledin & John Schoenmakers, 2020. "Semitractability of optimal stopping problems via a weighted stochastic mesh algorithm," Mathematical Finance, Wiley Blackwell, vol. 30(4), pages 1591-1616, October.
    7. Chinonso Nwankwo & Weizhong Dai & Tony Ware, 2023. "Enhancing accuracy for solving American CEV model with high-order compact scheme and adaptive time stepping," Papers 2309.03984, arXiv.org, revised Sep 2023.

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