Abstract
We use new fully functional methods to describe and study the dynamics of the short-term interest rate process in continuous-time. The suggested procedure exploits the spatial properties, embodied in the local time process, of the diffusion of interest, and is robust against deviations from stationarity. Our results indicate that the misspecification of a standard constant elasticity of variance model with linear mean-reverting drift cannot be attributed to the nonlinear behavior of the infinitesimal first moment of the short-term interest rate process at high rates. Rather, it should be attributed to the martingale nature of the process over most of its empirical range (i.e., between 3% and about 15%).
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