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Valuing American Put Options Using Chebyshev Polynomial Approximation

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Author Info
Guglielmo Maria Caporale ()
Mario Cerrato

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Abstract

This pa per suggests a simple valuation method based on Chebyshev approximation at Chebyshev nodes to value American put options. It is similar to the approach taken in Sullivan (2000), where the option`s continuation region function is estimated by using a Chebyshev polynomial. However, in contrast to Sullivan (2000), the functional is fitted by using Chebyshev nodes. The suggested method is flexible, easy to program and efficient, and can be extended to price other types of derivative instruments. It is also applicable in other fields, providing efficient solutions to complex systems of partial differential equations. The paper also describes an alternative method based on dynamic programming and backward induction to approximate the option value in each time period.

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File URL: http://www.brunel.ac.uk/329/efwps/05-03.pdf
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Paper provided by Economics and Finance Section, School of Social Sciences, Brunel University in its series Economics and Finance Discussion Papers with number 05-03.

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Length: 23 pages
Date of creation: Feb 2005
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Handle: RePEc:bru:bruedp:05-03

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Postal: Brunel University, Uxbridge, Middlesex UB8 3PH, UK

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  1. Longstaff, Francis A & Schwartz, Eduardo S, 2001. "Valuing American Options by Simulation: A Simple Least-Squares Approach," Review of Financial Studies, Oxford University Press for Society for Financial Studies, vol. 14(1), pages 113-47.
  2. Cox, John C. & Ross, Stephen A. & Rubinstein, Mark, 1979. "Option pricing: A simplified approach," Journal of Financial Economics, Elsevier, vol. 7(3), pages 229-263, September. [Downloadable!] (restricted)
  3. Dixit, Avinash, 1992. "Investment and Hysteresis," Journal of Economic Perspectives, American Economic Association, vol. 6(1), pages 107-32, Winter. [Downloadable!] (restricted)
  4. Sullivan, Michael A, 2000. "Valuing American Put Options Using Gaussian Quadrature," Review of Financial Studies, Oxford University Press for Society for Financial Studies, vol. 13(1), pages 75-94.
  5. Geske, Robert & Johnson, Herb E, 1984. " The American Put Option Valued Analytically," Journal of Finance, American Finance Association, vol. 39(5), pages 1511-24, December. [Downloadable!] (restricted)
  6. Manuel Moreno & Javier R. Navas, 2001. "On the Robustness of Least-Squares Monte Carlo (LSM) for Pricing American Derivatives," Economics Working Papers 543, Department of Economics and Business, Universitat Pompeu Fabra. [Downloadable!]
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  7. Abadir, Karim M. & Rockinger, Michael, 2003. "Density Functionals, With An Option-Pricing Application," Econometric Theory, Cambridge University Press, vol. 19(05), pages 778-811, October. [Downloadable!]
  8. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-54, May-June. [Downloadable!] (restricted)
  9. Barone-Adesi, Giovanni & Whaley, Robert E, 1987. " Efficient Analytic Approximation of American Option Values," Journal of Finance, American Finance Association, vol. 42(2), pages 301-20, June. [Downloadable!] (restricted)
  10. Lars Stentoft, 2004. "Assessing the Least Squares Monte-Carlo Approach to American Option Valuation," Review of Derivatives Research, Springer, vol. 7(2), pages 129-168, 08. [Downloadable!]
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