Is the Drift of the Interest Rate Process Linear? A New Approach and Evidence

Abstract

Continuous-time models are important for investigating interest rate term structure and pricing fixed income derivatives. Economic theory often provides little guidance on the choice of the form of continuous-time models, and existing one-factor and multi-factor continuous-time interest rate models often assume a linear drift, among other things. Some studies, based smoothed nonparametric kernel estimation, suggest that the drift of the interest rate process is nonlinear, particularly at high interest rate levels. However, this has been doubted as an artifact of smoothed nonparametric estimation in comparison with highly persistent interest rate data. Whether the drift of the interest rate process is linear or nonlinear remains an unsolved issue in the literature. In this paper, we take a new approach to re-address this important issue by first considering a general continuous-time regression for the interest rate process and then testing it via a generalized spectral derivative approach of Hong and Lee (2005) which is tailored to the continuous-time setting. Our method avoids the undesirable features of smoothed nonparametric estimation for highly persistent financial time series data. Unlike the existing approaches to testing linearity in drift, we allow for stochastic volatility and jumps, which have been well documented for the interest rate process in the literature. An empirically realistic simulation study shows that the generalized spectral derivative provides reliable inference in finite samples for continuous-time models. Based on the widely used 7-day Eurodollar rates, we document strong evidence that the interest rate process has a nonlinear drift and such evidence is robust to the presence of level effect, stochastic volatility, jumps, and different methods of drift parameter estimation. We further document that such popular nonlinear drift models as Aït-Sahalia's (1996a) nonlinear drift model and Ahn and Gao's (1991) Inverse-Feller drift model can capture some nonlinear drift dynamics of the short rate, and Aït-Sahalia's nonlinear model outperforms Ahn and Gao's nonlinear drift model due to its flexibility to capture asymmetric mean-reverting feature. However, they are still firmly rejected, indicating room for further improving the modelling of the drift function of the interest rate.