Comparing Maximum Likelihood and Generalized Method of Moments in Short Term Interest Rate Models

Abstract

In this thesis we will look at some different continuous models for predicting the short term interest rate, and focus on the method of parameter estimation in such models. A particular focus will be placed on the method of Maximum Likelihood Estimation (MLE), which has not been the most common method of estimation in this context. Furthermore, we will compare MLE to the Generalized Method of Moments (GMM), and both methods will be used in simulation experiments and on different sets of real data. Our starting point for investigation will be the model used in Chan et al.(1992), a model in which several of the most popular short rate models can be nested. We will use a discrete-valued approximation of this model to facilitate the estimation of parameters. In conclusion, this thesis argues that the MLE method of parameter estimation in short term interest rate models deserves more attention than it is currently given. In simulation experiments, the MLE method produced more accurate and precise estimates than the GMM method. Specifically, the bias in estimating the mean-reversion parameter is smaller using the MLE method. These results are particularly interesting as the GMM method is currently the common approach to parameter estimation in short term interest rate models. However, as will be shown in this thesis, it may very well be that the MLE method constitutes a better approach than GMM for such estimations. The results in this thesis may therefore contribute to the theoretical perspective as well as the real-world applications of methods of parameter estimation in predicting the short term interest rate.