Maximum Likelihood Estimation of the Cox-Ingersoll-Ross Model Using Particle Filters

This paper shows how to build in a computationally efficient way a maximum simulated likelihood procedure to estimate the Cox-Ingersoll-Ross model from multivariate time series. The advantage of this estimator is that it takes into account the exact likelihood function while avoiding the huge computational burden associated with MCMC methods and without the ad hoc assumption that certain bond yields are measured without error. The proposed methodology is implemented and tested on simulated data. For realistic parameter values the estimator seems to have good small sample properties, compared to the popular quasi maximum likelihood approach, even using moderate simulation sizes. The effect of simulation errors does not seem to undermine the estimation procedure.