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

Abstract

Abstract We study convergence properties of the full truncation Euler scheme for the Cox–Ingersoll–Ross (CIR) 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 $L^{p}$ 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 CIR process based on sequential evaluations of the driving Brownian motion.