Pricing American Options: A Duality Approach

40 Pages Posted: 5 Feb 2002

See all articles by Martin Brendan Haugh

Martin Brendan Haugh

Imperial College Business School

Leonid Kogan

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

Multiple version iconThere are 2 versions of this paper

Date Written: December 2001

Abstract

We develop a new method for pricing American options. The main practical contribution of this paper is a general algorithm for constructing upper and lower bounds on the true price of the option using any approximation to the option price. We show that our bounds are tight, so that if the initial approximation is close to the true price of the option, the bounds are also guaranteed to be close. We also explicitly characterize the worst-case performance of the pricing bounds. The computation of the lower bound is straightforward and relies on simulating the suboptimal exercise strategy implied by the approximate option price. The upper bound is also computed using Monte Carlo simulation. This is made feasible by the representation of the American option price as a solution of a properly defined dual minimization problem, which is the main theoretical result of this paper. Our algorithm proves to be accurate on a set of sample problems where we price call options on the maximum and the geometric mean of a collection of stocks. These numerical results suggest that our pricing method can be successfully applied to problems of practical interest.

Keywords: Asset pricing, dynamic programming, simulation, American option, optimal stopping, duality

JEL Classification: G12, G13

Suggested Citation

Haugh, Martin Brendan and Kogan, Leonid, Pricing American Options: A Duality Approach (December 2001). Mit Sloan Working Paper No. 4340-01. Available at SSRN: https://ssrn.com/abstract=294821 or http://dx.doi.org/10.2139/ssrn.294821

Martin Brendan Haugh

Imperial College Business School ( email )

South Kensington Campus
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London SW7 2AZ, SW7 2AZ
United Kingdom

Leonid Kogan (Contact Author)

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

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Cambridge, MA 02142
United States
617-253-2289 (Phone)
617-258-6855 (Fax)

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

National Bureau of Economic Research (NBER)

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Cambridge, MA 02138
United States

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