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Calculating The Early Exercise Boundary Of American Put Options With An Approximation Formula

Author

Listed:
  • SONG-PING ZHU

    (School of Mathematics and Applied Statistics, University of Wollongong, Wollongong, NSW 2522, Australia)

  • ZHI-WEI HE

    (Faculty of Business, Ninbo University, Ninbo, Zhejiang, 315211, P. R. China)

Abstract

Accurately as well as efficiently calculating the early exercise boundary is the key to the highly nonlinear problem of pricing American options. Many analytical approximations have been proposed in the past, aiming at improving the computational efficiency and the easiness of using the formula, while maintaining a reasonable numerical accuracy at the same time. In this paper, we shall present an approximation formula based on Bunch and Johnson's work [6]. After clearly pointing out some errors in Bunch and Johnson's paper [6], we will propose an improved approximation formula that can significantly enhance the computational accuracy, particularly for options of long lifetime.

Suggested Citation

  • Song-Ping Zhu & Zhi-Wei He, 2007. "Calculating The Early Exercise Boundary Of American Put Options With An Approximation Formula," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 10(07), pages 1203-1227.
    • Handle: RePEc:wsi:ijtafx:v:10:y:2007:i:07:n:s0219024907004615
    DOI: 10.1142/S0219024907004615
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    Citations

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    Cited by:

    1. Jun Cheng & Jin Zhang, 2012. "Analytical pricing of American options," Review of Derivatives Research, Springer, vol. 15(2), pages 157-192, July.
    2. Medvedev, Alexey & Scaillet, Olivier, 2010. "Pricing American options under stochastic volatility and stochastic interest rates," Journal of Financial Economics, Elsevier, vol. 98(1), pages 145-159, October.
    3. Song-Ping Zhu & Nhat-Tan Le & Wen-Ting Chen & Xiaoping Lu, 2015. "Pricing Parisian down-and-in options," Papers 1511.01564, arXiv.org.
    4. Minqiang Li, 2010. "A quasi-analytical interpolation method for pricing American options under general multi-dimensional diffusion processes," Review of Derivatives Research, Springer, vol. 13(2), pages 177-217, July.
    5. Tomas Bokes, 2010. "A unified approach to determining the early exercise boundary position at expiry for American style of general class of derivatives," Papers 1012.0348, arXiv.org, revised Mar 2011.
    6. Zafar Ahmad & Reilly Browne & Rezaul Chowdhury & Rathish Das & Yushen Huang & Yimin Zhu, 2023. "Fast American Option Pricing using Nonlinear Stencils," Papers 2303.02317, arXiv.org, revised Oct 2023.

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