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Minimal realizations of interest rate models

  • Tomas BjÃrk

    ()

    (Department of Finance, Stockholm School of Economics, Box 6501, SE-113 83 Stockholm Sweden)

  • Andrea Gombani

    ()

    (LADSEB-CNR, Corso Stati Uniti 4, I-35127 Padova, Italy Manuscript)

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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Article provided by Springer in its journal Finance and Stochastics.

Volume (Year): 3 (1999)
Issue (Month): 4 ()
Pages: 413-432

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Handle: RePEc:spr:finsto:v:3:y:1999:i:4:p:413-432
Note: received: July 1997; final version received: December 1998
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