() and Andrea Gombani
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.
34 pages, August 19, 1997
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