A Multinomial Approximation for American Option Prices in Levy Process Models

21 Pages Posted: 31 Aug 2006

See all articles by Ross Maller

Ross Maller

Australian National University (ANU) - School of Finance and Applied Statistics

David Solomon

University of Chicago

Alexander Szimayer

University of Hamburg - Faculty of Economics and Business Administration

Abstract

This paper gives a tree-based method for pricing American options in models where the stock price follows a general exponential Levy process. A multinomial model for approximating the stock price process, which can be viewed as generalizing the binomial model of Cox, Ross, and Rubinstein (1979) for geometric Brownian motion, is developed. Under mild conditions, it is proved that the stock price process and the prices of American-type options on the stock, calculated from the multinomial model, converge to the corresponding prices under the continuous time Lévy process model. Explicit illustrations are given for the variance gamma model and the normal inverse Gaussian process when the option is an American put, but the procedure is applicable to a much wider class of derivatives including some path-dependent options. Our approach overcomes some practical difficulties that have previously been encountered when the Lévy process has infinite activity.

Suggested Citation

Maller, Ross and Solomon, David and Szimayer, Alexander, A Multinomial Approximation for American Option Prices in Levy Process Models. Mathematical Finance, Vol. 16, No. 4, pp. 613-633, October 2006. Available at SSRN: https://ssrn.com/abstract=927843 or http://dx.doi.org/10.1111/j.1467-9965.2006.00286.x

Ross Maller (Contact Author)

Australian National University (ANU) - School of Finance and Applied Statistics ( email )

Canberra, Australian Capital Territory 0200
Australia

David Solomon

University of Chicago ( email )

1101 East 58th Street
Chicago, IL 60637
United States

Alexander Szimayer

University of Hamburg - Faculty of Economics and Business Administration ( email )

Von-Melle-Park 5
Hamburg, 20146
Germany

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