Pricing Perpetual American Option Under L evy Process: A Mellin Transform Approach

Abstract

We propose a Mellin transform method to numerically compute the prices and greeks of American option driven by a class of Levy processes under incomplete market with Follmer Schweizer minimal measure. We develop a partial integro-differential l equation(PIDE) for American option and applied Mellin transform on it. Subsequently we perform the inversion of these Mellin transform to construct an approximation of the prices and sensitivities of American options in a class of Levy models. The class includes many of the Levy process employed in quantitative finance such as the NIG, CGMY and Meixner models.