Scandinavian Working Papers in Economics

SSE/EFI Working Paper Series in Economics and Finance,
Stockholm School of Economics

No 182: Minimal Realizations of Forward Rates

Tomas Björk () and Andrea Gombani ()
Additional contact information
Tomas Björk: Dept. of Finance, Stockholm School of Economics, Postal: P.O. Box 6501, S-113 83 Stockholm, Sweden
Andrea Gombani: LADSEB-CNR, Postal: Corso Stati Uniti 4, I-35127 Padova, Italy

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.

JEL-codes: E43; G13

34 pages, August 19, 1997

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