Strong order 1/2 convergence of full truncation Euler approximations to the Cox-Ingersoll-Ross process

We study convergence properties of the full truncation Euler scheme for the Cox–Ingersoll–Ross process in the regime where the boundary point zero is inaccessible. Under some conditions on the model parameters (precisely, when the so-called Feller ratio is greater than three), we establish the strong order 1/2 convergence in Lp of the scheme to the exact solution. For the global error criterion studied in this paper, this is consistent with the optimal rate of strong convergence for approximations to the Cox–Ingersoll– Ross process based on sequential evaluations of the driving Brownian motion.