Simple simulation schemes for cir and Wishart processes

We develop some simple simulation algorithms for CIR and Wishart processes. We investigate rigorously the square of a matrix valued Ornstein-Uhlenbeck process, the main idea being to split the generator and to reduce the problem to the simulation of the square of a matrix valued Ornstein-Uhlenbeck process to be added to a deterministic process. In this way, we provide a weak second-order scheme that requires only the simulation of i.i.d. Gaussian r.v.'s and simple matrix manipulations.