On the discretization schemes for the CIR (and Bessel squared) processes

In this paper, we focus on the simulation of the Cox-Ingersoll-Ross processes and present several discretization schemes of both the implicit and explicit types. We study their strong and weak convergence. We also examine numerically their behaviour and compare them to the schemes already proposed by Deelstra and Delbaen [5] and Diop [6]. Finally, we gather all the results obtained and recommend, in the standard case, the use of one of our explicit schemes.