In this paper we study and implement a finite difference version of the augmented state variable approach proposed by Hull & White (1993) that allows for pathdependent securities. We apply the method to a class of path-dependent interest rate derivatives and consider several examples including mortgage backed securities and collateralized mortgage obligations. The efficiency of the method is assessed in a comparative study with Monte Carlo simulation and we find it to be faster for a similar accuracy.
By Mikkel Svenstrup