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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.

Suggested Citation

  • 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, August.
  • Handle: RePEc:kap:revdev:v:7:y:2004:i:2:p:129-168
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    Cited by:

    1. Carmona, Julio & León, Angel & Vaello-Sebastià, Antoni, 2011. "Pricing executive stock options under employment shocks," Journal of Economic Dynamics and Control, Elsevier, pages 97-114.
    2. Yu, Xisheng & Xie, Xiaoke, 2015. "Pricing American options: RNMs-constrained entropic least-squares approach," The North American Journal of Economics and Finance, Elsevier, vol. 31(C), pages 155-173.
    3. Caporale, Guglielmo Maria & Cerrato, Mario, 2008. "Chebyshev polynomial approximation to approximate partial differential equations," SIRE Discussion Papers 2008-15, Scottish Institute for Research in Economics (SIRE).
    4. 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.
    5. Lihua Zhang & Weiguo Zhang & Weijun Xu & Xiang Shi, 2014. "A Modified Least-Squares Simulation Approach to Value American Barrier Options," Computational Economics, Springer;Society for Computational Economics, vol. 44(4), pages 489-506, December.
    6. Gabriel J Power & Charli D. Tandja M. & Josée Bastien & Philippe Grégoire, 2015. "Measuring infrastructure investment option value," Journal of Risk Finance, Emerald Group Publishing, vol. 16(1), pages 49-72, January.
    7. Nelson Areal & Artur Rodrigues & Manuel Armada, 2008. "On improving the least squares Monte Carlo option valuation method," Review of Derivatives Research, Springer, pages 119-151.
    8. Stentoft, Lars, 2005. "Pricing American options when the underlying asset follows GARCH processes," Journal of Empirical Finance, Elsevier, vol. 12(4), pages 576-611, September.
    9. Rombouts, Jeroen & Stentoft, Lars & Violante, Franceso, 2014. "The value of multivariate model sophistication: An application to pricing Dow Jones Industrial Average options," International Journal of Forecasting, Elsevier, pages 78-98.
    10. 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.
    11. Andrea Gamba & Nicola Fusari, 2009. "Valuing Modularity as a Real Option," Management Science, INFORMS, pages 1877-1896.
    12. Carmona, Julio & León, Angel & Vaello-Sebastià, Antoni, 2012. "Does stock return predictability affect ESO fair value?," European Journal of Operational Research, Elsevier, vol. 223(1), pages 188-202.
    13. Mario Cerrato, 2008. "Valuing American Derivatives by Least Squares Methods," Working Papers 2008_12, Business School - Economics, University of Glasgow, revised Sep 2008.
    14. 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.
    15. Berridge, S.J. & Schumacher, J.M., 2002. "An Irregular Grid Approach for Pricing High Dimensional American Options," Discussion Paper 2002-99, Tilburg University, Center for Economic Research.
    16. Stentoft, Lars, 2011. "American option pricing with discrete and continuous time models: An empirical comparison," Journal of Empirical Finance, Elsevier, vol. 18(5), pages 880-902.
    17. Minqiang Li, 2010. "A quasi-analytical interpolation method for pricing American options under general multi-dimensional diffusion processes," Review of Derivatives Research, Springer, pages 177-217.
    18. Joseph Y. J. Chow & Hamid R. Sayarshad, 2016. "Reference Policies for Non-myopic Sequential Network Design and Timing Problems," Networks and Spatial Economics, Springer, vol. 16(4), pages 1183-1209, December.
    19. Ravi Kashyap, 2016. "Securities Lending Strategies, Valuation of Term Loans using Option Theory," Papers 1609.01274, arXiv.org, revised Nov 2016.
    20. Jin, Xing & Yang, Cheng-Yu, 2016. "Efficient estimation of lower and upper bounds for pricing higher-dimensional American arithmetic average options by approximating their payoff functions," International Review of Financial Analysis, Elsevier, vol. 44(C), pages 65-77.
    21. Katarzyna Toporek, 2012. "Simple is better. Empirical comparison of American option valuation methods," Ekonomia journal, Faculty of Economic Sciences, University of Warsaw, vol. 29.
    22. Engesaeth, E.J.P., 2011. "Managerial compensation contracting," Other publications TiSEM 5eb8d152-e701-4e5c-8852-7, Tilburg University, School of Economics and Management.
    23. Zhu, Lei & Zhang, ZhongXiang & Fan, Ying, 2015. "Overseas oil investment projects under uncertainty: How to make informed decisions?," Journal of Policy Modeling, Elsevier, vol. 37(5), pages 742-762.
    24. Lars Stentoft, 2013. "American option pricing using simulation with an application to the GARCH model," Chapters,in: Handbook of Research Methods and Applications in Empirical Finance, chapter 5, pages 114-147 Edward Elgar Publishing.
    25. Michael Ludkovski, 2015. "Kriging Metamodels and Experimental Design for Bermudan Option Pricing," Papers 1509.02179, arXiv.org, revised Oct 2016.

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