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




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1 CERMICS - Centre d-Enseignement et de Recherche en Mathématiques et Calcul Scientifique 2 MATHFI - Financial mathematics Inria Paris-Rocquencourt, ENPC - École des Ponts ParisTech, UPEC UP12 - Université Paris-Est Créteil Val-de-Marne - Paris 12

Abstract : 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.

Keywords : simulation discretization scheme squared Bessel process Cox-Ingersoll-Ross model Heston model Affine Term Structure Models ATSM





Author: Aurélien Alfonsi -

Source: https://hal.archives-ouvertes.fr/



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