Is the Short Rate Drift Actually Nonlinear?

Abstract

Virtually all existing continuous-time, single-factor term structure models are based on a short rate process that has a linear drift function. However, there is no strong a priori argument in favor of linearity, and Stanton (1997) and Ait-Sahalia (1996), employing nonparametric estimation techniques, conclude that the drift function contains important nonlinearities. Comparatively little is known about the finite-sample properties of these estimators, particularly when they are applied to frequent sampling of a very persistent process, like short term interest rates. We apply these estimators to simulated sample paths of a square-root diffusion. Although the drift function is linear, both estimators suggest nonlinearities of the type and magnitude reported in by Stanton (1997) and Ait-Sahalia (1996). These results, along with the results of a weighted least squares estimation procedure applied to the Stanton and Ait-Sahalia data sets, imply that nonlinearity of the short rate drift is not a robust stylized fact.