Optimization and Systems Theory Seminar
March 21, 1997, 11.00-12.00

Tomas Björk
Department of Finance,
Stockholm School of Economics

Some system theoretic aspects of interest rate theory

Using system theoretic ideas we try to understand when an infinite dimensional stochastic process, like the forward rate curve in an interest rate model, actually evolves on a finite dimensional submanifold of the full Banach space of forward rate curves. We try to answer the following questions.

• Given a specific interest rate model (e.g. the Hull-White model) and a fixed finite dimensional submanifold of forward curves (e.g. the Nelson-Siegel family), What are the necessary and sufficient conditions for the submanifold to be invariant under the action of the forward rate dynamics?
• Take as given a concrete interest rate model. Does there exist a finitely parameterized family of forward curves which is invariant under the action of the interest rate model?