On the Existence of Finite Dimensional Realizations for Nonlinear Forward Rate Models
AbstractWe consider interest rate models of Heath-Jarrow-Morton type, where the forward rates are driven by a multidimensional Wiener process, and where the volatility is allowed to be an arbitrary smooth functional of the present forward rate curve. Using ideas from differential geometry as well as from systems and control theory, we investigate when the forward rate process can be realized by a finite dimensional Markovian state space model, and we give general necessary and sufficient conditions, in terms of the volatility structure, for the existence of a finite dimensional realization. A number of concrete applications are given, and most previously known realization results for time homogenous Wiener driven models are included and extended. As a special case we give a general and easily applicable necessary and sufficient condition for when the induced short rate is a Markov porcess. In particular we show that the only forward rate models, with short rate dependent volatility structures, which generically give rise to a Markovian short rate are the affine ones. These models are thus the only generic short rate models from a forward rate point of view.
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Bibliographic InfoPaper provided by Stockholm School of Economics in its series Working Paper Series in Economics and Finance with number 338.
Length: 46 pages
Date of creation: 22 Oct 1999
Date of revision:
Publication status: Published in Mathematical Finance, 2001, pages 205-243.
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Forward rate curves; interest rate models; factor models; state space models; Markovian realizations;
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
This paper has been announced in the following NEP Reports:
- NEP-ALL-2000-01-24 (All new papers)
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