Simulation of the CIR Process

Up to now, computers are only able to do deterministic tasks and they cannot generate true random numbers. To sample random numbers, they run deterministic sequences called pseudorandom number generators that produce a sequence of real numbers in [0, 1] that behaves like a sequence of independent random variables that are distributed uniformly on [0, 1]. Different families of pseudorandom number generators exist. It is important to use generators that have a large period, such as the Mersenne twister. In fact, running a Monte-Carlo algorithm to compute pathwise expectations may use intensively the generator. The convergence of the Monte-Carlo algorithm is degraded when the amount of pseudorandom numbers used is close or larger than the period.