  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 Feller ratio is greater than three), we establish the strong order 1/2
convergence in $L^{p}$ of the scheme to the exact solution. This is consistent
with the optimal rate of strong convergence for Euler approximations of
stochastic differential equations with globally Lipschitz coefficients, despite
the fact that the diffusion coefficient in the Cox-Ingersoll-Ross model is not
Lipschitz.
