On Finite-dimensional Term Structure models

Details On Finite-dimensional Term Structure models On Finite-dimensional Term Structure models

2002-01-22

arxiv.org/abs/math/0201204v1

Mathematics

Probability

Scientific paper

In this paper we provide the characterization of all finite-dimensional Heath--Jarrow--Morton models that admit arbitrary initial yield curves. It is well known that affine term structure models with time-dependent coefficients (such as the Hull--White extension of the Vasicek short rate model) perfectly fit any initial term structure. We find that such affine models are in fact the only finite-factor term structure models with this property. We also show that there is usually an invariant singular set of initial yield curves where the affine term structure model becomes time-homogeneous. We also argue that other than functional dependent volatility structures -- such as local state dependent volatility structures -- cannot lead to finite-dimensional realizations. Finally, our geometric point of view is illustrated by several examples.

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