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The Economic Research Institute, Stockholm School of Economics SSE/EFI Working Paper Series in Economics and Finance

No 182:
Minimal Realizations of Forward Rates

Tomas Björk () and Andrea Gombani ()

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.; (follow links to similar papers)

JEL-Codes: E43; G13; (follow links to similar papers)

34 pages, August 19, 1997

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This paper is published as:
Björk, Tomas and Andrea Gombani, (1999), 'Minimal Realizations of Forward Rates', Finance and Stochastics, Vol. 3, No. 4, pages 413-432

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