Minimal Realizations of Interest Rate Models

Posted: 21 Sep 1999

See all articles by Tomas Bjork

Tomas Bjork

Stockholm School of Economics - Swedish House of Finance

Andrea Gombani

Italian National Research Council (CNR) - Institute for Systems Science and Biomedical Engineering (LADSEB)

Abstract

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.

JEL Classification: E43, G13

Suggested Citation

Bjork, Tomas and Gombani, Andrea, Minimal Realizations of Interest Rate Models. Finance and Stochastics, Vol. 3, Iss. 4, August 1999. Available at SSRN: https://ssrn.com/abstract=179554

Tomas Bjork (Contact Author)

Stockholm School of Economics - Swedish House of Finance ( email )

Drottninggatan 98
111 60 Stockholm
Sweden

Andrea Gombani

Italian National Research Council (CNR) - Institute for Systems Science and Biomedical Engineering (LADSEB) ( email )

Corso Stati Uniti 4
I-35127 Padova
Italy

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