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Valuing American Put Options Using Gaussian Quadrature

Author

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  • Sullivan, Michael A

Abstract

This article develops an efficient and accurate method for numerical evaluation of the integral equation which defines the American put option value function. Numerical integration using Gaussian quadrature and function approximation using Chebyshev polynomials are combined to evaluate recursive expectations and produce an approximation of the option value function in two dimensions, across stock prices and over time to maturity. A set of such solutions results in a multidimensional approximation that is extremely accurate and very quick to compute. The method is an effective alternative to finite difference methods, the binomial model, and various analytic approximations. Article published by Oxford University Press on behalf of the Society for Financial Studies in its journal, The Review of Financial Studies.

Suggested Citation

  • Sullivan, Michael A, 2000. "Valuing American Put Options Using Gaussian Quadrature," Review of Financial Studies, Society for Financial Studies, vol. 13(1), pages 75-94.
  • Handle: RePEc:oup:rfinst:v:13:y:2000:i:1:p:75-94
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    Cited by:

    1. repec:spr:fininn:v:2:y:2016:i:1:d:10.1186_s40854-016-0042-9 is not listed on IDEAS
    2. Barone-Adesi, Giovanni, 2005. "The saga of the American put," Journal of Banking & Finance, Elsevier, vol. 29(11), pages 2909-2918, November.
    3. repec:bla:irvfin:v:16:y:2016:i:4:p:647-658 is not listed on IDEAS
    4. Caporale, Guglielmo Maria & Cerrato, Mario, 2008. "Chebyshev polynomial approximation to approximate partial differential equations," SIRE Discussion Papers 2008-15, Scottish Institute for Research in Economics (SIRE).
    5. Minqiang Li, 2010. "Analytical approximations for the critical stock prices of American options: a performance comparison," Review of Derivatives Research, Springer, vol. 13(1), pages 75-99, April.
    6. 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.
    7. Geonwoo Kim & Hyuncheul Lim & Sungchul Lee, 2015. "On pricing options with stressed-beta in a reduced form model," Review of Derivatives Research, Springer, vol. 18(1), pages 29-50, April.
    8. Antonio Cosma & Stefano Galluccio & Paola Pederzoli & O. Scaillet, 2016. "Early Exercise Decision in American Options with Dividends, Stochastic Volatility and Jumps," Swiss Finance Institute Research Paper Series 16-73, Swiss Finance Institute.
    9. repec:eee:dyncon:v:88:y:2018:i:c:p:1-20 is not listed on IDEAS
    10. 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.
    11. Antonio Cosma & Stefano Galluccio & Paola Pederzoli & O. Scaillet, "undated". "Valuing American Options Using Fast Recursive Projections," Swiss Finance Institute Research Paper Series 12-26, Swiss Finance Institute.
    12. Chung, San-Lin & Shih, Pai-Ta, 2009. "Static hedging and pricing American options," Journal of Banking & Finance, Elsevier, vol. 33(11), pages 2140-2149, November.
    13. S. G. Kou & Hui Wang, 2004. "Option Pricing Under a Double Exponential Jump Diffusion Model," Management Science, INFORMS, vol. 50(9), pages 1178-1192, September.
    14. Antonella Basso & Martina Nardon & Paolo Pianca, 2004. "A two-step simulation procedure to analyze the exercise features of American options," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 27(1), pages 35-56, August.
    15. Doobae Jun & Hyejin Ku, 2013. "Valuation of American partial barrier options," Review of Derivatives Research, Springer, vol. 16(2), pages 167-191, July.
    16. A. Sullivan, Michael, 2001. "Discrete-time continuous-state interest rate models," Journal of Economic Dynamics and Control, Elsevier, vol. 25(6-7), pages 1001-1017, June.
    17. Andricopoulos, Ari D. & Widdicks, Martin & Duck, Peter W. & Newton, David P., 2003. "Universal option valuation using quadrature methods," Journal of Financial Economics, Elsevier, vol. 67(3), pages 447-471, March.

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