PROJECTING THE FORWARD RATE FLOW ONTO A FINITE DIMENSIONAL MANIFOLD

Abstract

Given a Heath–Jarrow–Morton (HJM) interest rate model [Formula: see text] and a parametrized family of finite dimensional forward rate curves [Formula: see text], this paper provides a technique for projecting the infinite dimensional forward rate curve rt given by [Formula: see text] onto the finite dimensional manifold [Formula: see text]. The Stratonovich dynamics of the projected finite dimensional forward curve are derived and it is shown that, under the regularity conditions, the given Stratonovich differential equation has a unique strong solution. Moreover, this projection leads to an efficient algorithm for implicit parametric estimation of the infinite dimensional HJM model. The feasibility of this method is demonstrated by applying the generalized method of moments.