Projecting the Forward Rate Flow onto a Finite Dimensional Manifold

Details Projecting the Forward Rate Flow onto a Finite Dimensional Manifold Projecting the Forward Rate Flow onto a Finite Dimensional Manifold

2005-09-10

arxiv.org/abs/cs/0509028v1

Computer Science

Computational Engineering, Finance, and Science

To appear in the International Journal of Theoretical and Applied Finance

Scientific paper

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.

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