On the Geometry of Interest Rate Models
AbstractIn this paper, which is a substantial extension of the earlier essay Björk (2001), we give an overview of some recent work on the geometric properties of the evolution of the forward rate curve in an arbitrage free bond market. The main problems to be discussed are as follows. 1. When is a given forward rate model consistent with a given family of forward rate curves? 2. When can the inherently infinite dimensional forward rate process be realized by means of a Markovian finite dimensional state space model. We consider interest rate models of Heath-Jarrow-Morton type, where the forward rates are driven by a multidimensional Wiener process, and where he volatility is allowed to be an arbitrary smooth functional of the present forward rate curve. Within this framework we give necessary and sufficient conditions for consistency, as well as for the existence of a finite dimensional realization, in terms of the forward rate volatilities. We also study stochastic volatility HJM models, and we provide a systematic method for the construction of concrete realizations.
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Bibliographic InfoPaper provided by Stockholm School of Economics in its series Working Paper Series in Economics and Finance with number 545.
Length: 87 pages
Date of creation: 24 Nov 2003
Date of revision:
Note: To apppear in "Springer Lecture Notes in Mathematics"
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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-2003-11-30 (All new papers)
- NEP-CBA-2003-11-30 (Central Banking)
- NEP-FIN-2003-11-30 (Finance)
- NEP-MON-2003-11-30 (Monetary Economics)
- NEP-RMG-2003-11-30 (Risk Management)
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
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Working Paper Series
53, Finance Discipline Group, UTS Business School, University of Technology, Sydney.
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Research Paper Series
5, Quantitative Finance Research Centre, University of Technology, Sydney.
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