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. (C) 2009 IMACS. Published by Elsevier, B.V. All rights reserved.