EXPONENTIAL INTEGRABILITY PROPERTIES OF EULER DISCRETIZATION SCHEMES FOR THE COX-INGERSOLL-ROSS PROCESS

We study exponential integrability properties of the Cox-Ingersoll Ross (CIR) process and its Euler-Maruyama discretizations with various types of truncation and reflection at 0. These properties play a key role in establishing the finiteness of moments and the strong convergence of numerical approximations for a class of stochastic differential equations arising in finance. We prove that both implicit and explicit Euler-Maruyama discretizations for the CIR process preserve the exponential integrability of the exact solution for a wide range of parameters, and find lower bounds on the explosion time.