On Finite-dimensional Term Structure Models

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.