On the Existence of Finite Dimensional Realizations for Nonlinear Forward Rate Models

Tomas Bjork and Lars Svensson ()
Additional contact information
Lars Svensson: Department of Mathematics, Postal: Royal Institute of Technology, S-100 44 Stockholm, Sweden

No 338, SSE/EFI Working Paper Series in Economics and Finance from Stockholm School of Economics

Abstract: We 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.

Keywords: Forward rate curves; interest rate models; factor models; state space models; Markovian realizations (search for similar items in EconPapers)
JEL-codes: E43 G13 (search for similar items in EconPapers)
Pages: 46 pages
Date: 1999-10-22
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (26)

Published in Mathematical Finance, 2001, pages 205-243.

Downloads: (external link)
http://swopec.hhs.se/hastef/papers/hastef0338.pdf.zip (application/pdf)
http://swopec.hhs.se/hastef/papers/hastef0338.pdf (application/pdf)
http://swopec.hhs.se/hastef/papers/hastef0338.ps.zip (application/postscript)
http://swopec.hhs.se/hastef/papers/hastef0338.ps (application/postscript)

Related works:
Journal Article: On the Existence of Finite‐Dimensional Realizations for Nonlinear Forward Rate Models (2001)
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hhs:hastef:0338

Access Statistics for this paper

More papers in SSE/EFI Working Paper Series in Economics and Finance from Stockholm School of Economics The Economic Research Institute, Stockholm School of Economics, P.O. Box 6501, 113 83 Stockholm, Sweden. Contact information at EDIRC.
Bibliographic data for series maintained by Helena Lundin ().