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High order discretization schemes for the CIR process: Application to affine term structure and Heston models

This paper presents weak second and third order schemes for the Cox-Ingersoll-Ross (CIR) process, without any restriction on its parameters. At the same time, it gives a general recursive construction method to get weak second-order schemes that extends the one introduced by Ninomiya and Victoir~\cite{NV}. Combining these both results, this allows to propose a second-order scheme for more general affine diffusions. Simulation examples are given to illustrate the convergence of these schemes on CIR and Heston models. Algorithms are stated in a pseudocode language.