Evaluation of American option prices in a path integral framework using Fourier-Hermite series expansions

In this paper we review the path integral technique which has wide applicat ions in statistical physics and relate it to the backward recursion techniq ue which is widely used for the evaluation of derivative securities. We for mulate the pricing of equity options, both European and American, using the path integral framework. Discretising in the time variable and using expan sions in Fourier-Hermite series for the continuous representation of the un derlying asset price, we show how these options can be evaluated in the pat h integral framework. For American options, the solution technique facilita tes the accurate determination of the early exercise boundary as part of th e solution. Additionally, the continuous representation of the state variab le allows the relatively accurate and efficient evaluation of the option pr ices and the delta hedge ratio. (C) 1999 Elsevier Science B.V. All rights r eserved.