Path Dependent Option Pricing: The Path Integral Partial Averaging Method

Abstract

In this paper I develop a new computational method for pricing path dependent options. Using the path integral representation of the option price, I show that in general it is possible to perform analytically a partial averaging over the underlying risk-neutral diffusion process. This result greatly eases the computational burden placed on the subsequent numerical evaluation. For short-medium term options it leads to a general approximation formula that only requires the evaluation of a one dimensional integral. I illustrate the application of the method to Asian options and occupation time derivatives.

Keywords: derivatives, option, path dependent, path integral

JEL Classification: G13, C63