High order discretization schemes for the CIR process: application to Affine Term Structure and Heston models

Aurélien Alfonsi (1, 2)

1 CERMICS - Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique
2 MATHFI - Financial mathematics

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.

Mots clés: simulation; discretization scheme; squared Bessel process; Cox-Ingersoll-Ross model; Heston model; Affine Term Structure Models (ATSM)

Domaines: Probabilités [math.PR]

Aurélien Alfonsi. High order discretization schemes for the CIR process: application to Affine Term Structure and Heston models. Mathematics of Computation, 2010, 79 (269), pp.209-237. ⟨10.1090/S0025-5718-09-02252-2⟩. ⟨hal-00143723v5⟩