On the equivalence of a class of affine term structure models

In specifying a finite factor model for the term structure of interest rates, one usually begins by modeling the dynamics of the underlying factors. In most cases, this is sufficient to completely determine the term structure model. However, a point that is often overlooked is that seemingly different specifications of the factor dynamics may generate indistinguishable term structure models, in the sense that they produce pathwise identical bond prices. Consequently, it is important to be able to determine, at the level of factor dynamics, the conditions under which the models they generate are indistinguishable. In the case of time-homogeneous affine term structure models (ATSMs), such conditions were first described in Dai and Singleton (J Finance 55:1943–1978, 2000). In this paper, we formalize and extend their results to a class of time-inhomogeneous ATSMs, and obtain a simple method for determining the indistinguishability of these models in terms of the underlying factor dynamics.