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Assessing the Least Squares Monte-Carlo Approach to American Option Valuation

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  • Lars Stentoft

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Abstract

A detailed analysis of the Least Squares Monte-Carlo (LSM) approach to American option valuation suggested in Longstaff and Schwartz (2001) is performed. We compare the specification of the cross-sectional regressions with Laguerre polynomials used in Longstaff and Schwartz (2001) with alternative specifications and show that some of these have numerically better properties. Furthermore, each of these specifications leads to a trade-off between the time used to calculate a price and the precision of that price. Comparing the method-specific trade-offs reveals that a modified specification using ordinary monomials is preferred over the specification based on Laguerre polynomials. Next, we generalize the pricing problem by considering options on multiple assets and we show that the LSM method can be implemented easily for dimensions as high as ten or more. Furthermore, we show that the LSM method is computationally more efficient than existing numerical methods. In particular, when the number of assets is high, say five, Finite Difference methods are infeasible, and we show that our modified LSM method is superior to the Binomial Model.

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Bibliographic Info

Article provided by Springer in its journal Review of Derivatives Research.

Volume (Year): 7 (2004)
Issue (Month): 2 (08)
Pages: 129-168

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Handle: RePEc:kap:revdev:v:7:y:2004:i:2:p:129-168

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Web page: http://www.springerlink.com/link.asp?id=102989

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Cited by:
  1. Berridge, S.J. & Schumacher, J.M., 2004. "An Irregular Grid Approach for Pricing High-Dimensional American Options," Discussion Paper 2004-18, Tilburg University, Center for Economic Research.
  2. Mario Cerrato & Kan Kwok Cheung, 2007. "Valuing American Style Options by Least Squares Methods," Money Macro and Finance (MMF) Research Group Conference 2006 49, Money Macro and Finance Research Group.
  3. Boyer, M. Martin & Stentoft, Lars, 2013. "If we can simulate it, we can insure it: An application to longevity risk management," Insurance: Mathematics and Economics, Elsevier, vol. 52(1), pages 35-45.
  4. Carmona, Julio & León, Angel & Vaello-Sebastiá, Antoni, 2011. "Does Stock Return Predictability Affect ESO Fair Value?," QM&ET Working Papers 11-2, Universidad de Alicante, Departamento de Métodos Cuantitativos y Teoría Económica, revised 16 Jan 2012.
  5. Jeroen V.K. Rombouts & Lars Stentoft & Francesco Violante, 2012. "The Value of Multivariate Model Sophistication: An Application to pricing Dow Jones Industrial Average options," CREATES Research Papers 2012-04, School of Economics and Management, University of Aarhus.
  6. Mario Cerrato, 2008. "Valuing American Derivatives by Least Squares Methods," Working Papers 2008_12, Business School - Economics, University of Glasgow, revised Sep 2008.
  7. Engesaeth, E.J.P., 2011. "Managerial compensation contracting," Open Access publications from Tilburg University urn:nbn:nl:ui:12-4807459, Tilburg University.
  8. 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.
  9. 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.
  10. 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.
  11. Guglielmo Maria Caporale & Mario Cerrato, 2008. "Chebyshev polynomial approximation to approximate partial differential equations," Working Papers 2008_16, Business School - Economics, University of Glasgow.
  12. Katarzyna Toporek, 2012. "Simple is better. Empirical comparison of American option valuation methods," Ekonomia journal, Faculty of Economic Sciences, University of Warsaw, vol. 29.

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