### 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.
*