Projecting the Forward Rate Flow onto a Finite Dimensional Manifold

TL;DR

This paper introduces a method to project infinite-dimensional forward rate curves from HJM models onto finite-dimensional manifolds, enabling efficient estimation and analysis of interest rate dynamics.

Contribution

It provides a novel projection technique for HJM forward curves onto finite-dimensional manifolds and derives the associated Stratonovich dynamics for improved modeling.

Findings

Derived the Stratonovich dynamics for the projected forward rate curves.

Proposed an efficient algorithm for parametric estimation of HJM models.

Validated the approach using the generalized method of moments.

Abstract

Given a Heath-Jarrow-Morton (HJM) interest rate model $\mathcal{M}$ and a parametrized family of finite dimensional forward rate curves $\mathcal{G}$, this paper provides a technique for projecting the infinite dimensional forward rate curve $r_{t}$ given by $\mathcal{M}$ onto the finite dimensional manifold $\mathcal{G}$.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.