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Valuing American Put Options Using Gaussian Quadrature

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  • Sullivan, Michael A
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    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.

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    Bibliographic Info

    Article provided by Society for Financial Studies in its journal Review of Financial Studies.

    Volume (Year): 13 (2000)
    Issue (Month): 1 ()
    Pages: 75-94

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    Handle: RePEc:oup:rfinst:v:13:y:2000:i:1:p:75-94

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    Cited by:
    1. 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.
    2. Minqiang Li, Li, 2009. "Analytical Approximations for the Critical Stock Prices of American Options: A Performance Comparison," MPRA Paper 15018, University Library of Munich, Germany.
    3. Li, Minqiang, 2009. "A Quasi-analytical Interpolation Method for Pricing American Options under General Multi-dimensional Diffusion Processes," MPRA Paper 17348, University Library of Munich, Germany.
    4. 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.
    5. 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.
    6. 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, vol. 27(1), pages 35-56, 08.
    7. Doobae Jun & Hyejin Ku, 2013. "Valuation of American partial barrier options," Review of Derivatives Research, Springer, vol. 16(2), pages 167-191, July.
    8. 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.
    9. Barone-Adesi, Giovanni, 2005. "The saga of the American put," Journal of Banking & Finance, Elsevier, vol. 29(11), pages 2909-2918, November.

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