SSE/EFI Working Paper Series in Economics and Finance
On the Geometry of Interest Rate Models
Abstract: In 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
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
Keywords: Forward rate curves; interest rate models; factor models; state space models; Markovian realizations; (follow links to similar papers)
JEL-Codes: E43; G13; (follow links to similar papers)
87 pages, November 24, 2003
To apppear in "Springer Lecture Notes in Mathematics"
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