Minimal Realizations of Forward Rates
AbstractWe 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.
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Bibliographic InfoPaper provided by Stockholm School of Economics in its series Working Paper Series in Economics and Finance with number 182.
Length: 34 pages
Date of creation: 19 Aug 1997
Date of revision:
Publication status: Published in Finance and Stochastics, 1999, pages 413-432.
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More information through EDIRC
Interest rates; realization theory; factor models.;
Find related papers by JEL classification:
- E43 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Interest Rates: Determination, Term Structure, and Effects
- G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
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