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Richardson extrapolation techniques for the pricing of American‐style options

Author

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  • Chuang‐Chang Chang
  • San‐Lin Chung
  • Richard C. Stapleton

Abstract

In this article, the authors reexamine the American‐style option pricing formula of R. Geske and H.E. Johnson (1984), and extend the analysis by deriving a modified formula that can overcome the possibility of nonuniform convergence (which is likely to occur for nonstandard American options whose exercise boundary is discontinuous) encountered in the original Geske–Johnson methodology. Furthermore, they propose a numerical method, the Repeated‐Richardson extrapolation, which allows the estimation of the interval of true option values and the determination of the number of options needed for an approximation to achieve a given desired accuracy. Using simulation results, our modified Geske–Johnson formula is shown to be more accurate than the original Geske–Johnson formula for pricing American options, especially for nonstandard American options. This study also illustrates that the Repeated‐Richardson extrapolation approach can estimate the interval of true American option values extremely well. Finally, the authors investigate the possibility of combining the binomial Black–Scholes method proposed by M. Broadie and J.B. Detemple (1996) with the Repeated‐Richardson extrapolation technique. © 2007 Wiley Periodicals, Inc. Jrl Fut Mark 27:791–817, 2007

Suggested Citation

  • Chuang‐Chang Chang & San‐Lin Chung & Richard C. Stapleton, 2007. "Richardson extrapolation techniques for the pricing of American‐style options," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 27(8), pages 791-817, August.
    • Handle: RePEc:wly:jfutmk:v:27:y:2007:i:8:p:791-817
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    Cited by:

    1. Chan, Tat Lung (Ron), 2020. "Hedging and pricing early-exercise options with complex fourier series expansion," The North American Journal of Economics and Finance, Elsevier, vol. 54(C).
    2. Jia‐Hau Guo & Lung‐Fu Chang, 2020. "Repeated Richardson extrapolation and static hedging of barrier options under the CEV model," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 40(6), pages 974-988, June.
    3. Gong, Xiaoli & Zhuang, Xintian, 2017. "American option valuation under time changed tempered stable Lévy processes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 466(C), pages 57-68.
    4. Ballestra, Luca Vincenzo & Cecere, Liliana, 2015. "Pricing American options under the constant elasticity of variance model: An extension of the method by Barone-Adesi and Whaley," Finance Research Letters, Elsevier, vol. 14(C), pages 45-55.
    5. Guillaume Leduc, 2024. "The Boyle–Romberg Trinomial Tree, a Highly Efficient Method for Double Barrier Option Pricing," Mathematics, MDPI, vol. 12(7), pages 1-15, March.
    6. Tafirenyika Sunde & Olusegun A. Akanbi, 2016. "Sources of unemployment in Namibia: an application of the structural VAR approach," International Journal of Sustainable Economy, Inderscience Enterprises Ltd, vol. 8(2), pages 125-143.
    7. Ballestra, Luca Vincenzo & Cecere, Liliana, 2016. "A numerical method to estimate the parameters of the CEV model implied by American option prices: Evidence from NYSE," Chaos, Solitons & Fractals, Elsevier, vol. 88(C), pages 100-106.
    8. Alessandro Andreoli & Luca Vincenzo Ballestra & Graziella Pacelli, 2018. "Pricing Credit Default Swaps Under Multifactor Reduced-Form Models: A Differential Quadrature Approach," Computational Economics, Springer;Society for Computational Economics, vol. 51(3), pages 379-406, March.
    9. Jiefei Yang & Guanglian Li, 2023. "On Sparse Grid Interpolation for American Option Pricing with Multiple Underlying Assets," Papers 2309.08287, arXiv.org, revised Sep 2023.
    10. Golbabai, Ahmad & Mohebianfar, Ehsan, 2017. "A new method for evaluating options based on multiquadric RBF-FD method," Applied Mathematics and Computation, Elsevier, vol. 308(C), pages 130-141.
    11. A. Golbabai & E. Mohebianfar, 2017. "A New Stable Local Radial Basis Function Approach for Option Pricing," Computational Economics, Springer;Society for Computational Economics, vol. 49(2), pages 271-288, February.
    12. Tat Lung & Chan, 2019. "An SFP--FCC Method for Pricing and Hedging Early-exercise Options under L\'evy Processes," Papers 1909.07319, arXiv.org.
    13. 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.
    14. Rad, Jamal Amani & Parand, Kourosh & Ballestra, Luca Vincenzo, 2015. "Pricing European and American options by radial basis point interpolation," Applied Mathematics and Computation, Elsevier, vol. 251(C), pages 363-377.

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