Maximum Likelihood Estimation of Non-Linear Continuous-Time Term-Structure Models

Abstract

This paper presents an exact maximum likelihood method which is designed for estimating multi-dimensional time-homogeneous diffusion processes, using discretely sampled observations. The essence of this method is to evaluate the transition density by means of simulating the diffusion processes. The advantages of this approach are that we do not have to derive the distribution for the diffusion process described by the stochastic differential equation, and that we can use all the standard results from the likelihood theory. We apply this exact maximum likelihood method to consider a class of dynamic one factor continuous-time interest rate models all nested within the CKLS-model (Chan, Karolyi, Longstaff and Sanders 1992), which will enable us to compare the different models. The general superiority of this method to existing methods (e.g. QML, GMM) is documented through Monte Carlo studies. We also show that the method can be applied with great benefit to multi-factor continuous-time term-structure models, and we look at a non-linear special case of the Brennan & Schwartz model (1982). Finally, empirical results from the U.S. market will be presented. NOTE: This is a revised version of the paper Estimation of a Dynamic One Factor Continuous-Time Term-Structure Model.