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On the Robustness of Least-Squares Monte Carlo (LSM) for Pricing American Derivatives

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Author Info
Manuel Moreno
Javier R. Navas

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Abstract

This paper analyses the robustness of Least-Squares Monte Carlo, a technique recently proposed by Longstaff and Schwartz (2001) for pricing American options. This method is based on least-squares regressions in which the explanatory variables are certain polynomial functions. We analyze the impact of different basis functions on option prices. Numerical results for American put options provide evidence that a) this approach is very robust to the choice of different alternative polynomials and b) few basis functions are required. However, these conclusions are not reached when analyzing more complex derivatives.

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Paper provided by Department of Economics and Business, Universitat Pompeu Fabra in its series Economics Working Papers with number 543.

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Date of creation: Apr 2001
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Handle: RePEc:upf:upfgen:543

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Related research
Keywords: Least-Squares Monte Carlo; option pricing; American options;

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Find related papers by JEL classification:
C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Statistical Simulation Methods
C60 - Mathematical and Quantitative Methods - - Mathematical Methods and Programming - - - General
G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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  1. Bunch, David S & Johnson, Herb, 1992. " A Simple and Numerically Efficient Valuation Method for American Puts Using a Modified Geske-Johnson Approach," Journal of Finance, American Finance Association, vol. 47(2), pages 809-16, June. [Downloadable!] (restricted)
  2. Brennan, Michael J & Schwartz, Eduardo S, 1977. "The Valuation of American Put Options," Journal of Finance, American Finance Association, vol. 32(2), pages 449-62, May. [Downloadable!] (restricted)
  3. Schwartz, Eduardo S., 1977. "The valuation of warrants: Implementing a new approach," Journal of Financial Economics, Elsevier, vol. 4(1), pages 79-93, January. [Downloadable!] (restricted)
  4. Parkinson, Michael, 1977. "Option Pricing: The American Put," Journal of Business, University of Chicago Press, vol. 50(1), pages 21-36, January. [Downloadable!] (restricted)
  5. Roll, Richard, 1977. "An analytic valuation formula for unprotected American call options on stocks with known dividends," Journal of Financial Economics, Elsevier, vol. 5(2), pages 251-258, November. [Downloadable!] (restricted)
  6. 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)
  7. Ju, Nengjiu, 1998. "Pricing an American Option by Approximating Its Early Exercise Boundary as a Multipiece Exponential Function," Review of Financial Studies, Oxford University Press for Society for Financial Studies, vol. 11(3), pages 627-46.
  8. Boyle, Phelim P., 1988. "A Lattice Framework for Option Pricing with Two State Variables," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 23(01), pages 1-12, March. [Downloadable!]
  9. Huang, Jing-zhi & Subrahmanyam, Marti G & Yu, G George, 1996. "Pricing and Hedging American Options: A Recursive Integration Method," Review of Financial Studies, Oxford University Press for Society for Financial Studies, vol. 9(1), pages 277-300. [Downloadable!] (restricted)
  10. Boyle, Phelim P., 1977. "Options: A Monte Carlo approach," Journal of Financial Economics, Elsevier, vol. 4(3), pages 323-338, May. [Downloadable!] (restricted)
  11. Kim, In Joon, 1990. "The Analytic Valuation of American Options," Review of Financial Studies, Oxford University Press for Society for Financial Studies, vol. 3(4), pages 547-72. [Downloadable!] (restricted)
  12. Robert C. Merton, 1973. "Theory of Rational Option Pricing," Bell Journal of Economics, The RAND Corporation, vol. 4(1), pages 141-183, Spring. [Downloadable!] (restricted)
  13. Barraquand, J?r?me & Martineau, Didier, 1995. "Numerical Valuation of High Dimensional Multivariate American Securities," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 30(03), pages 383-405, September. [Downloadable!]
  14. Rendleman, Richard J, Jr & Bartter, Brit J, 1979. "Two-State Option Pricing," Journal of Finance, American Finance Association, vol. 34(5), pages 1093-1110, December. [Downloadable!] (restricted)
  15. Ho, T S & Stapleton, Richard C & Subrahmanyam, Marti G, 1997. " The Valuation of American Options with Stochastic Interest Rates: A Generalization of the Geske-Johnson Technique," Journal of Finance, American Finance Association, vol. 52(2), pages 827-40, June. [Downloadable!] (restricted)
  16. Johnson, H. E., 1983. "An Analytic Approximation for the American Put Price," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 18(01), pages 141-148, March. [Downloadable!]
  17. 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)
  18. David S. Bunch & Herb Johnson, 2000. "The American Put Option and Its Critical Stock Price," Journal of Finance, American Finance Association, vol. 55(5), pages 2333-2356, October. [Downloadable!] (restricted)
  19. Breen, Richard, 1991. "The Accelerated Binomial Option Pricing Model," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 26(02), pages 153-164, June. [Downloadable!]
  20. Carr, Peter, 1998. "Randomization and the American Put," Review of Financial Studies, Oxford University Press for Society for Financial Studies, vol. 11(3), pages 597-626.
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Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Guglielmo Maria Caporale & Mario Cerrato, 2005. "Valuing American Put Options Using Chebyshev Polynomial Approximation," Economics and Finance Discussion Papers 05-03, Economics and Finance Section, School of Social Sciences, Brunel University. [Downloadable!]
    Other versions:
  2. 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. [Downloadable!]
  3. Nelson Areal & Artur Rodrigues & Manuel Armada, 2008. "On improving the least squares Monte Carlo option valuation method," Review of Derivatives Research, Springer, vol. 11(1), pages 119-151, March. [Downloadable!] (restricted)
  4. Berridge, S.J. & Schumacher, J.M., 2002. "An irregular grid approach for pricing high-dimensional American options," Discussion Paper 99, Tilburg University, Center for Economic Research. [Downloadable!]
    Other versions:
  5. Alexander Boogert & Cyriel de Jong, 2007. "Gas Storage Valuation Using a Monte Carlo Method," Birkbeck Working Papers in Economics and Finance 0704, Birkbeck, Department of Economics, Mathematics & Statistics. [Downloadable!]
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