Optimal Martingales and American Option Pricing
AbstractPricing American options is an interesting research topic since there is no analytical solution to value these derivatives. Different numerical methods have been proposed in the literature with some, if not all, either limited to a specific payoff or not applicable to multidimensional cases. Applications of Monte Carlo methods to price American options is a relatively new area that started with Longstaff and Schwartz (2001). Since then, few variations of that methodology have been proposed. The general conclusion is that Monte Carlo estimators tend to underestimate the true option price. The present paper follows Glasserman and Yu (2004b) and proposes a novel Monte Carlo approach, based on designing "optimal martingales" to determine stopping times. We show that our martingale approach can also be used to compute the dual as described in Rogers (2002).
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Bibliographic InfoPaper provided by Scottish Institute for Research in Economics (SIRE) in its series SIRE Discussion Papers with number 2008-36.
Date of creation: 2008
Date of revision:
American options; Monte Carlo method;
Other versions of this item:
- Cerrato, Mario & Abbasyan, Abdollah, 2009. "Optimal Martingales and American Option Pricing," SIRE Discussion Papers 2009-38, 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.
- G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)
- G14 - Financial Economics - - General Financial Markets - - - Information and Market Efficiency; Event Studies; Insider Trading
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- L. C. G. Rogers, 2002. "Monte Carlo valuation of American options," Mathematical Finance, Wiley Blackwell, vol. 12(3), pages 271-286.
- Barone-Adesi, Giovanni & Whaley, Robert E, 1987. " Efficient Analytic Approximation of American Option Values," Journal of Finance, American Finance Association, vol. 42(2), pages 301-20, June.
- Mario Cerrato, 2008.
"Valuing American Derivatives by Least Squares Methods,"
2008_12, Business School - Economics, University of Glasgow, revised Sep 2008.
- Cerrato, Mario, 2008. "Valuing American Derivatives by Least Squares Methods," SIRE Discussion Papers 2008-44, Scottish Institute for Research in Economics (SIRE).
- 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.
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