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Mathematics of Computation

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

Author: Aurélien Alfonsi
Journal: Math. Comp. 79 (2010), 209-237
MSC (2000): Primary 60H35, 65C30; Secondary 91B70
Published electronically: June 15, 2009
MathSciNet review: 2552224
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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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Additional Information

Aurélien Alfonsi
Affiliation: CERMICS, MATHFI Project, Ecole des Ponts, 6-8 avenue Blaise Pascal, Cité Descartes, Champs sur Marne, 77455 Marne-la-vallée, France

Keywords: Simulation, discretization scheme, squared Bessel process, Cox-Ingersoll-Ross model, Heston model, Affine Term Structure Models (ATSM)
Received by editor(s): October 24, 2008
Received by editor(s) in revised form: December 16, 2008
Published electronically: June 15, 2009
Additional Notes: Most of this work was done when I was at the TU Berlin, thanks to the support of MATHEON. I would like to thank Vlad Bally (Univ. Marne-la-Vallée) and Benjamin Jourdain (Ecole des Ponts) for fruitful comments, and Victor Reutenauer (CALyon) for stimulating discussions on ATSM
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.