Minimal realizations of interest rate models

Tomas BjÃrk () and Andrea Gombani ()
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Tomas BjÃrk: Department of Finance, Stockholm School of Economics, Box 6501, SE-113 83 Stockholm Sweden
Andrea Gombani: LADSEB-CNR, Corso Stati Uniti 4, I-35127 Padova, Italy Manuscript
Authors registered in the RePEc Author Service: Tomas Bjork

Finance and Stochastics, 1999, vol. 3, issue 4, 413-432

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.

Keywords: Interest rates; realization theory; factor models (search for similar items in EconPapers)
JEL-codes: E43 G13 (search for similar items in EconPapers)
Date: 1999-08-20
Note: received: July 1997; final version received: December 1998
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Citations: View citations in EconPapers (24)

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