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Optimal martingales and American option pricing

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  • Mario Cerrato
  • Abdollah Abbasyan

Abstract

Pricing American options is an interesting research topic since there is no ana- lytical solution to value these derivatives. Di¤erent numerical methods have been proposed in the literature with some, if not all, either limited to a speci c payo¤ or not applicable to multidimensional cases. Applications of Monte Carlo meth- ods to price American options is a relatively new area that started with Longsta¤ and Schwartz (2001). Since then, few variations of that methodology have been pro- posed. 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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Paper provided by Business School - Economics, University of Glasgow in its series Working Papers with number 2009_27.

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Date of creation: Jul 2009
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Handle: RePEc:gla:glaewp:2009_27

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Keywords: American options; Monte Carlo method;

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  1. Mario Cerrato, 2008. "Valuing American Derivatives by Least Squares Methods," Working Papers 2008_12, Business School - Economics, University of Glasgow, revised Sep 2008.
  2. L. C. G. Rogers, 2002. "Monte Carlo valuation of American options," Mathematical Finance, Wiley Blackwell, vol. 12(3), pages 271-286.
  3. 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.
  4. 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.
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