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A MULTINOMIAL APPROXIMATION FOR AMERICAN OPTION PRICES IN LÉVY PROCESS MODELS
Author(s) -
Maller Ross A.,
Solomon David H.,
Szimayer Alex
Publication year - 2006
Publication title -
mathematical finance
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.98
H-Index - 81
eISSN - 1467-9965
pISSN - 0960-1627
DOI - 10.1111/j.1467-9965.2006.00286.x
Subject(s) - binomial options pricing model , lévy process , geometric brownian motion , multinomial distribution , econometrics , exponential function , inverse gaussian distribution , trinomial tree , mathematical economics , mathematics , variance gamma distribution , economics , cox process , stock (firearms) , brownian motion , valuation of options , diffusion process , poisson process , statistics , mathematical analysis , mechanical engineering , engineering , economy , distribution (mathematics) , poisson distribution , estimator , asymptotic distribution , service (business)
This paper gives a tree‐based method for pricing American options in models where the stock price follows a general exponential Lévy 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.