Path dependent option pricing: the path integral partial averaging method
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.