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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

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


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:
  • 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
  • © Copyright 2009 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Math. Comp. 79 (2010), 209-237
  • MSC (2000): Primary 60H35, 65C30; Secondary 91B70
  • DOI:
  • MathSciNet review: 2552224