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

Alfonsi, Aurélien

doi:10.1090/S0025-5718-09-02252-2

High order discretization schemes for the CIR process: Application to affine term structure and Heston models
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Math. Comp. 79 (2010), 209-237 Request permission

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 for getting weak second order schemes that extend the one introduced by Ninomiya and Victoir. Combine both these results, this allows us 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.

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