On Short Rate Processes and Their Implications for Term Structure Movements

We compare short rate diffusion models with respect to their implications for term structure movements, the plausiblity of which serves us as a criterion for evaluating the models. Analytically for Gauss-Markov models and numerically for a broader collection of models prevalent in the literature, we isolate the deformations of the term structure generated endogenously. Among other analytical tools we use spread options on the forward rate curve as an aggregate measure of term structure shapes across states. On the basis of our analysis we conclude that the Ho/Lee model should be discarded, since it cannot explain the emergence of downward sloping term structures, that the introduction of mean reversion is essential in order to generate downward sloping term structures in any substantial proportion, that the models typically favor upward sloping term structures for short maturities and downward sloping term structures for longer maturities, and that there is a surprisingly strong similarity among many of the models prevalent in the literature. A model which allows arbitrary boundaries for the short rate realizations to be fixed exogenously completes our analysis.