Projecting the Forward Rate Flow on a Finite Dimensional Manifold

Given an Heath-Jarrow-Morton (HJM) interest rate model and a parametrized family of finite dimensional forward rate curves, this paper provides us a way to project this infinite dimensional HJM forward rate curve to the finite dimensional manifold. This projection characterizes banks' behavior of calibrating forward curves by applying a certain family of curves (e.g., Nelson-Seigel family). Moreover, we derive the Stratonovich dynamics of the projected finite dimensional forward curve. This leads an implicit algorithm for parametric estimation of the original HJM model. We have demonstrated the feasibility of this method by applying generalized method of moments and methods of simulated moments.