Minimal Realizations of Forward Rates

Tomas Bjork and Andrea Gombani ()
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Andrea Gombani: LADSEB-CNR, Postal: Corso Stati Uniti 4, I-35127 Padova, Italy

No 182, SSE/EFI Working Paper Series in Economics and Finance from Stockholm School of Economics

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 derivate prices.

Keywords: Interest rates; realization theory; factor models. (search for similar items in EconPapers)
JEL-codes: E43 G13 (search for similar items in EconPapers)
Pages: 34 pages
Date: 1997-08-19
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Citations: View citations in EconPapers (10)

Published in Finance and Stochastics, 1999, pages 413-432.

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