Itô Conditional Moment Generator and the Estimation of Short Rate Processes

Abstract

This paper exploits the Itô's formula to derive the conditional moments vector for the class of interest rate models that allow for nonlinear volatility and flexible jump specifications. Such a characterization of continuous-time processes by the Ito Conditional Moment Generator noticeably enlarges the admissible set beyond the affine jump-diffusion class. A simple GMM estimator can be constructed based on the analytical solution to the lower order moments, with natural diagnostics of the conditional mean, variance, skewness, and kurtosis. Monte Carlo evidence suggests that the proposed estimator has desirable finite sample properties, relative to the asymptotically efficient MLE. The empirical application singles out the nonlinear quadratic variance as the key feature of the U.S. short rate dynamics.