Optimization and Systems Theory Seminar
Friday, October 17, 1997, 11.00-12.00, Room 3721, Lindstedtsvägen 25

Tomas Björk
Department of Finance
Stockholm School of Economics
E-mail: fintb@hhs.se

Minimal realizations of forward rates

We consider interest rate models where the forward rates are allowed to be driven by a multidimensional Wiener process as well as by a marked point process. Assuming a deterministic volatility structure, and using ideas from systems and control theory, we investigate when the input-output map generated by such a model can be realized by a finite dimensional stochastic differential equation. We give necessary and sufficient conditions, in terms of the given volatility structure, for the existence of a finite dimensional realization and we provide a formula for the determination of the dimension of a minimal realization. The abstract state space for a minimal realization is shown to have an immediate economic interpretation in terms of a minimal set of benchmark forward rates, and we give explicit formulas for bond prices in terms of the benchmark rates as well as for the computation of derivative prices.

Calendar of seminars
Last update: October 2, 1997 by Anders Forsgren, andersf@math.kth.se.