Uniform approximation of the Cox–Ingersoll–Ross process via exact simulation at random times

In this paper we uniformly approximate the trajectories of the Cox–Ingersoll–Ross (CIR) process. At a sequence of random times the approximate trajectories will be even exact. In between, the approximation will be uniformly close to the exact trajectory. From a conceptual point of view, the proposed method gives a better quality of approximation in a path-wise sense than standard, or even exact, simulation of the CIR dynamics at some deterministic time grid.