Pricing American Options: A Duality Approach

Operations Research, Forthcoming

Posted: 11 Mar 2003

See all articles by Leonid Kogan

Leonid Kogan

Massachusetts Institute of Technology (MIT) - Sloan School of Management; National Bureau of Economic Research (NBER)

Martin Brendan Haugh

Imperial College Business School

Multiple version iconThere are 2 versions of this paper

Abstract

American option pricing problem is one of the most computationally intensive problems in derivative pricing theory. The complications arise from the fact that the holder of the option has the right to exercise it at any one of the pre-specified exercise dates. Hence, to price such an option, one must solve an optimal stopping problem, which maximizes the value of the option over all possible exercise strategies. When applied to problems with multiple assets or realistic price dynamics, standard pricing algorithms suffer from the well-known curse of dimensionality. Several approximate pricing algorithms have been proposed in the literature in an attempt to use simulation methods to overcome the limitations of traditional pricing techniques. The accuracy of most such algorithms could not be rigorously evaluated, as they only provide a lower bound on the true option price. In "Pricing American Options: A Duality Approach", M. Haugh and L. Kogan develop a new duality theory for optimal stopping problems and use it to design a simulation method that allows one to compute the upper bounds on the true value of the American option price starting from any approximation to the option price. This simulation method possesses desirable tightness properties, i.e., as long as the initial approximation is close to the true option price, so is the upper bound. Since the algorithm does not depend on the specifics of how the initial approximation to the option price was obtained, it can be used in conjunction with any algorithm for approximating American option prices.

Note: This is a description of the paper and not the actual abstract.

JEL Classification: G12, G13

Suggested Citation

Kogan, Leonid and Haugh, Martin Brendan, Pricing American Options: A Duality Approach. Operations Research, Forthcoming. Available at SSRN: https://ssrn.com/abstract=380660

Leonid Kogan (Contact Author)

Massachusetts Institute of Technology (MIT) - Sloan School of Management ( email )

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HOME PAGE: http://web.mit.edu/lkogan2/www/

National Bureau of Economic Research (NBER)

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Martin Brendan Haugh

Imperial College Business School ( email )

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London SW7 2AZ, SW7 2AZ
United Kingdom

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