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A new numerical scheme for the CIR process

Author

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  • Halidias Nikolaos

    (Department of Mathematics, University of the Aegean, Karlovassi 83200 Samos, Greece)

Abstract

In this paper we generalize an explicit numerical scheme for the CIR process that we have proposed before. The advantage of the new proposed scheme is that preserves positivity and is well posed for a (little bit) broader set of parameters among the positivity preserving schemes. The order of convergence is at least logarithmic in general and for a smaller set of parameters is at least 1/4.

Suggested Citation

  • Halidias Nikolaos, 2015. "A new numerical scheme for the CIR process," Monte Carlo Methods and Applications, De Gruyter, vol. 21(3), pages 245-253, September.
    • Handle: RePEc:bpj:mcmeap:v:21:y:2015:i:3:p:245-253:n:1
    DOI: 10.1515/mcma-2015-0101
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    References listed on IDEAS

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    1. Gyöngy, István & Rásonyi, Miklós, 2011. "A note on Euler approximations for SDEs with Hölder continuous diffusion coefficients," Stochastic Processes and their Applications, Elsevier, vol. 121(10), pages 2189-2200, October.
    2. Alfonsi Aurélien, 2005. "On the discretization schemes for the CIR (and Bessel squared) processes," Monte Carlo Methods and Applications, De Gruyter, vol. 11(4), pages 355-384, December.
    3. Alfonsi, Aurélien, 2013. "Strong order one convergence of a drift implicit Euler scheme: Application to the CIR process," Statistics & Probability Letters, Elsevier, vol. 83(2), pages 602-607.
    4. John C. Cox & Jonathan E. Ingersoll Jr. & Stephen A. Ross, 2005. "A Theory Of The Term Structure Of Interest Rates," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 5, pages 129-164, World Scientific Publishing Co. Pte. Ltd..
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    Cited by:

    1. Nikolaos Halidias, 2016. "On construction of boundary preserving numerical schemes," Papers 1601.07864, arXiv.org, revised Feb 2016.

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