Two methods of estimation of the drift parameters of the Cox–Ingersoll–Ross process: Continuous observations

Abstract

We consider a stochastic differential equation of the form where a, b and σ are positive constants. The solution corresponds to the Cox–Ingersoll–Ross process. We study the estimation of an unknown drift parameter (a, b) by continuous observations of a sample path First, we prove the strong consistency of the maximum likelihood estimator. Since this estimator is well-defined only in the case we propose another estimator that is defined and strongly consistent for all positive a, b, σ. The quality of the estimators is illustrated by simulation results.