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High order discretization schemes for the CIR process: Application to affine term structure and Heston models
Author(s):
Aurélien
Alfonsi.
Journal:
Math. Comp.
79
(2010),
209-237.
MSC (2000):
Primary 60H35, 65C30;
Secondary 91B70
Posted:
June 15, 2009
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Additional information
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
Email:
alfonsi@cermics.enpc.fr
DOI:
10.1090/S0025-5718-09-02252-2
PII:
S 0025-5718(09)02252-2
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
Posted:
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
Copyright of article:
Copyright
2009,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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