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On the robustness of least-squares Monte Carlo (LSM) for pricing American derivatives

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  • Manuel Moreno
  • Javier R. Navas

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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Bibliographic Info

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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Web page: http://www.econ.upf.edu/

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

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  1. Cox, John C. & Ross, Stephen A. & Rubinstein, Mark, 1979. "Option pricing: A simplified approach," Journal of Financial Economics, Elsevier, Elsevier, vol. 7(3), pages 229-263, September.
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  15. Kim, In Joon, 1990. "The Analytic Valuation of American Options," Review of Financial Studies, Society for Financial Studies, Society for Financial Studies, vol. 3(4), pages 547-72.
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  17. Schwartz, Eduardo S., 1977. "The valuation of warrants: Implementing a new approach," Journal of Financial Economics, Elsevier, Elsevier, vol. 4(1), pages 79-93, January.
  18. Roll, Richard, 1977. "An analytic valuation formula for unprotected American call options on stocks with known dividends," Journal of Financial Economics, Elsevier, Elsevier, vol. 5(2), pages 251-258, November.
  19. 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, American Finance Association, vol. 52(2), pages 827-40, June.
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  22. Huang, Jing-zhi & Subrahmanyam, Marti G & Yu, G George, 1996. "Pricing and Hedging American Options: A Recursive Integration Method," Review of Financial Studies, Society for Financial Studies, Society for Financial Studies, vol. 9(1), pages 277-300.
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Citations

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Cited by:
  1. :Andrea Gamba & Fusari Nicola, 2009. "Valuing Modularity as a Real Option," Working Papers, Warwick Business School, Finance Group wpn09-03, Warwick Business School, Finance Group.
  2. Berridge, S.J. & Schumacher, J.M., 2004. "An Irregular Grid Approach for Pricing High-Dimensional American Options," Discussion Paper, Tilburg University, Center for Economic Research 2004-18, Tilburg University, Center for Economic Research.
  3. Minqiang Li, 2010. "A quasi-analytical interpolation method for pricing American options under general multi-dimensional diffusion processes," Review of Derivatives Research, Springer, Springer, vol. 13(2), pages 177-217, July.
  4. Carmona, Julio & León, Angel & Vaello-Sebastiá, Antoni, 2011. "Does Stock Return Predictability Affect ESO Fair Value?," QM&ET Working Papers, Universidad de Alicante, Departamento de Métodos Cuantitativos y Teoría Económica 11-2, Universidad de Alicante, Departamento de Métodos Cuantitativos y Teoría Económica, revised 16 Jan 2012.
  5. Andrea Gamba, 2002. "Real options Valuation: A Monte Carol Approach," Working Papers, Warwick Business School, Finance Group wpn02-02, Warwick Business School, Finance Group.
  6. Farid AitSahlia & Manisha Goswami & Suchandan Guha, 2010. "American option pricing under stochastic volatility: an efficient numerical approach," Computational Management Science, Springer, Springer, vol. 7(2), pages 171-187, April.
  7. Nelson Areal & Artur Rodrigues & Manuel Armada, 2008. "On improving the least squares Monte Carlo option valuation method," Review of Derivatives Research, Springer, Springer, vol. 11(1), pages 119-151, March.
  8. Alexander Boogert & Cyriel de Jong, 2007. "Gas Storage Valuation Using a Monte Carlo Method," Birkbeck Working Papers in Economics and Finance, Birkbeck, Department of Economics, Mathematics & Statistics 0704, Birkbeck, Department of Economics, Mathematics & Statistics.

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