Estimating continuous-time stochastic volatility models of the short-term interest rate

Abstract

We obtain consistent parameter estimates of continuous-time stochastic volatility diffusions for the U.S. risk-free short-term interest rate, sampled weekly over 1954–1995, using the Efficient Method of Moments procedure of Gallant and Tauchen. The preferred model displays mean reversion and incorporates 'level effects' and stochastic volatility in the diffusion function. Extensive diagnostics indicate that the Cox-Ingersoll-Ross model with an added stochastic volatility factor provides a good characterization of the short rate process. Further, they suggest that recently proposed GARCH models fail to approximate the discrete-time short rate dynamics, while 'Level-EGARCH' models perform reasonably well.