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Valuing American Derivatives by Least Squares Methods

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  • Mario Cerrato

Abstract

Least Squares estimators are notoriously known to generate sub-optimal exercise decisions when determining the optimal stopping time. The consequence is that the price of the option will be underestimated. We show how to use variance reduction techniques to extend some recent Monte Carlo estimators for option pricing and assess their performance in finite samples. Finally, we extend the Longstaff and Schwartz (2001) method to price American options under stochastic volatility. This is the first study to implement and apply the Glasserman and Yu (2004b) methodology to price Asian options and basket options.

Suggested Citation

  • Mario Cerrato, 2008. "Valuing American Derivatives by Least Squares Methods," Working Papers 2008_12, Business School - Economics, University of Glasgow, revised Sep 2008.
    • Handle: RePEc:gla:glaewp:2008_12
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    File URL: http://www.gla.ac.uk/media/media_73743_en.pdf
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    References listed on IDEAS

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    1. Boyle, Phelim & Broadie, Mark & Glasserman, Paul, 1997. "Monte Carlo methods for security pricing," Journal of Economic Dynamics and Control, Elsevier, vol. 21(8-9), pages 1267-1321, June.
    2. Lars Stentoft, 2004. "Convergence of the Least Squares Monte Carlo Approach to American Option Valuation," Management Science, INFORMS, vol. 50(9), pages 1193-1203, September.
    3. Mark Broadie & Menghui Cao, 2008. "Improved lower and upper bound algorithms for pricing American options by simulation," Quantitative Finance, Taylor & Francis Journals, vol. 8(8), pages 845-861.
    4. Luciano Fratocchi & Alberto Onetti & Alessia Pisoni & Marco Talaia, 2007. "Location of value added activities in hi-tech industries. The case of pharma-biotech firms in Italy," Economics and Quantitative Methods qf0708, Department of Economics, University of Insubria.
    5. Paul Glasserman & Bin Yu, 2005. "Large Sample Properties of Weighted Monte Carlo Estimators," Operations Research, INFORMS, vol. 53(2), pages 298-312, April.
    6. Philip Protter & Emmanuelle Clément & Damien Lamberton, 2002. "An analysis of a least squares regression method for American option pricing," Finance and Stochastics, Springer, vol. 6(4), pages 449-471.
    7. 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.
    8. L. C. G. Rogers, 2002. "Monte Carlo valuation of American options," Mathematical Finance, Wiley Blackwell, vol. 12(3), pages 271-286, July.
    9. Longstaff, Francis A & Schwartz, Eduardo S, 2001. "Valuing American Options by Simulation: A Simple Least-Squares Approach," University of California at Los Angeles, Anderson Graduate School of Management qt43n1k4jb, Anderson Graduate School of Management, UCLA.
    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, August.
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    Cited by:

    1. Cerrato, Mario & Abbasyan, Abdollah, 2008. "Optimal Martingales and American Option Pricing," SIRE Discussion Papers 2008-36, Scottish Institute for Research in Economics (SIRE).
    2. Ursula Silveira Monteiro de Lima & Carlos Patricio Samanez, 2016. "Complex derivatives valuation: applying the Least-Squares Monte Carlo Simulation Method with several polynomial basis," Financial Innovation, Springer;Southwestern University of Finance and Economics, vol. 2(1), pages 1-14, December.

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    More about this item

    Keywords

    American options; Monte Carlo method;

    JEL classification:

    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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