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On the discretization schemes for the CIR (and Bessel squared) processes

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  • Alfonsi Aurélien

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Abstract

In this paper, we focus on the simulation of the Cox-Ingersoll-Ross processes and present several discretization schemes of both the implicit and explicit types. We study their strong and weak convergence. We also examine numerically their behaviour and compare them to the schemes already proposed by Deelstra and Delbaen and Diop. Finally, we gather all the results obtained and recommend, in the standard case, the use of one of our explicit schemes.

Suggested Citation

  • 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.
    • Handle: RePEc:bpj:mcmeap:v:11:y:2005:i:4:p:355-384:n:5
    DOI: 10.1515/156939605777438569
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    References listed on IDEAS

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    1. 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..
    2. Damiano Brigo & Aurélien Alfonsi, 2005. "Credit default swap calibration and derivatives pricing with the SSRD stochastic intensity model," Finance and Stochastics, Springer, vol. 9(1), pages 29-42, January.
    3. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," The Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
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    Citations

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    Cited by:

    1. Roger Lord & Remmert Koekkoek & Dick Van Dijk, 2010. "A comparison of biased simulation schemes for stochastic volatility models," Quantitative Finance, Taylor & Francis Journals, vol. 10(2), pages 177-194.
    2. Lenkšas, A. & Mackevičius, V., 2015. "Weak approximation of Heston model by discrete random variables," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 113(C), pages 1-15.
    3. 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.
    4. Benjamin Jourdain & Mohamed Sbai, 2013. "High order discretization schemes for stochastic volatility models," Post-Print hal-00409861, HAL.
    5. Papin, Timothée, 2013. "Pricing of Corporate Loan : Credit Risk and Liquidity cost," Economics Thesis from University Paris Dauphine, Paris Dauphine University, number 123456789/12545 edited by Turinici, Gabriel.
    6. 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.
    7. Gilles Pag`es & Fabien Panloup, 2007. "Approximation of the distribution of a stationary Markov process with application to option pricing," Papers 0704.0335, arXiv.org, revised Sep 2009.
    8. Ke Du, 2013. "Commodity Derivative Pricing Under the Benchmark Approach," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 2, July-Dece.
    9. Ke Du & Eckhard Platen & Renata Rendek, 2012. "Modeling of Oil Prices," Research Paper Series 321, Quantitative Finance Research Centre, University of Technology, Sydney.
    10. repec:dau:papers:123456789/7818 is not listed on IDEAS
    11. 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.
    12. Andrei Cozma & Matthieu Mariapragassam & Christoph Reisinger, 2015. "Convergence of an Euler scheme for a hybrid stochastic-local volatility model with stochastic rates in foreign exchange markets," Papers 1501.06084, arXiv.org, revised Oct 2016.
    13. Halidias Nikolaos, 2015. "Constructing positivity preserving numerical schemes for the two-factor CIR model," Monte Carlo Methods and Applications, De Gruyter, vol. 21(4), pages 313-323, December.
    14. Timothée Papin & Gabriel Turinici, 2014. "Prepayment option of a perpetual corporate loan: the impact of the funding costs," Post-Print hal-00768571, HAL.
    15. Xianming Sun & Siqing Gan, 2014. "An Efficient Semi-Analytical Simulation for the Heston Model," Computational Economics, Springer;Society for Computational Economics, vol. 43(4), pages 433-445, April.
    16. Damiano Brigo & Naoufel El-Bachir, 2006. "Credit Derivatives Pricing with a Smile-Extended Jump Stochastic Intensity Model," ICMA Centre Discussion Papers in Finance icma-dp2006-13, Henley Business School, University of Reading.
    17. Timothée Papin & Gabriel Turinici, 2013. "Valuation of the Prepayment Option of a Perpetual Corporate Loan," Post-Print hal-00653041, HAL.
    18. Andreas Neuenkirch & Lukasz Szpruch, 2012. "First order strong approximations of scalar SDEs with values in a domain," Papers 1209.0390, arXiv.org.
    19. repec:hal:wpaper:hal-00768571 is not listed on IDEAS
    20. Paul Glasserman & Kyoung-Kuk Kim, 2011. "Gamma expansion of the Heston stochastic volatility model," Finance and Stochastics, Springer, vol. 15(2), pages 267-296, June.
    21. Eckhard Platen & Renata Rendek, 2009. "Exact Scenario Simulation for Selected Multi-dimensional Stochastic Processes," Research Paper Series 259, Quantitative Finance Research Centre, University of Technology, Sydney.
    22. Eckhard Platen & Renata Rendek, 2012. "The Affine Nature of Aggregate Wealth Dynamics," Research Paper Series 322, Quantitative Finance Research Centre, University of Technology, Sydney.
    23. S. Corsaro & P. De Angelis & Z. Marino & F. Perla, 2011. "Participating life insurance policies: an accurate and efficient parallel software for COTS clusters," Computational Management Science, Springer, vol. 8(3), pages 219-236, August.

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