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.
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Manuscript received: July 1997; final version received: December 1998
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Björk, T., Gombani, A. Minimal realizations of interest rate models. Finance Stochast 3, 413–432 (1999). https://doi.org/10.1007/s007800050069
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DOI: https://doi.org/10.1007/s007800050069