Maximum Likelihood Estimation of Continuous-Time Diffusion Models for Korean Short-Term Interest Rates

The purpose of this paper is to estimate a general continuous-time diffusion model for short term interest rates using Korean data. The model is general enough to encompass almost all of the diffusion models suggested in the literature to explain the dynamics of short term interest rates. We approximate the true but unknown conditional transition probability density function of the diffusion process using At-Sahalia's (2008) irreducible method to conduct maximum likelihood estimation. The overnight call rate and the 91 day CD rate have been adopted as a proxy for the short term interest rate. Overall, estimation results are quite similar for both interest rates. We could not find any significant evidence of nonlinearity in the drift in either data series. However, for both interest rates, a linear drift term is statistically different from zero at high interest rates. We could obtain very significant estimates for the parameters in the volatility function for all models and all data sets. The volatility term is an increasing function of the interest rates. We also found some evidence that the underlying data generating process might change over time.