On the valuation of interest rate products under multi-factor HJM term-structures

We consider the valuation of interest rate products with effected cash flow under a multifactor Heath-Jarrow-Morton (HJM) model of the term-structure of interest rates by hierarchical approximation. At the higher-level, we apply a stochastic spectral approximation of the forward rates and exhaust an indexed family of regularized Hamilton-Jacobi characterizations of the value function. At the lower-level, we utilize penalization and an extrapolation method-of-lines finite element method. Application to interest rate caps and an American discount bond option are considered in order to demonstrate the applicability of the method.