Valuing American Derivatives by Least Squares Methods
AbstractLeast 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.
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Bibliographic InfoPaper provided by Business School - Economics, University of Glasgow in its series Working Papers with number 2008_12.
Date of creation: Apr 2008
Date of revision: Sep 2008
American options; Monte Carlo method;
Other versions of this item:
- Cerrato, Mario, 2008. "Valuing American Derivatives by Least Squares Methods," SIRE Discussion Papers 2008-44, Scottish Institute for Research in Economics (SIRE).
- 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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- 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.
- L. C. G. Rogers, 2002. "Monte Carlo valuation of American options," Mathematical Finance, Wiley Blackwell, vol. 12(3), pages 271-286.
- 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.
- 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.
- 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.
- 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, 08.
- Cerrato, Mario & Abbasyan, Abdollah, 2008.
"Optimal Martingales and American Option Pricing,"
SIRE Discussion Papers
2008-36, Scottish Institute for Research in Economics (SIRE).
- Mario Cerrato & Abdollah Abbasyan, 2009. "Optimal martingales and American option pricing," Working Papers 2009_27, Business School - Economics, University of Glasgow.
- Cerrato, Mario & Abbasyan, Abdollah, 2009. "Optimal Martingales and American Option Pricing," SIRE Discussion Papers 2009-38, Scottish Institute for Research in Economics (SIRE).
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