A Parametric Non-Linear Model of Term Structure Dynamics

Recent nonparametric estimation studies pioneered by Ait-Sahalia (1996a, 1996b) document that the diffusion of the short rate is similar to the parametric function, r1.5, estimated by Chan, Karolyi, Longstaff, and Sanders (1992) whereas the drift is substantially nonlinear in the short rate. These empirical properties call into question the efficacy of the existing affine term structure models and beg for alternative models which admit the observed behavior. This paper presents such a model. Our model delivers closed-form solutions for bond prices and concave relationship between the interest rate and the yields. We show that in empirical analyses, our model outperforms the one-factor affine models in both time-series as well as cross-sectional tests