IDEAS home Printed from https://ideas.repec.org/a/bpj/mcmeap/v11y2005i4p355-384n5.html
   My bibliography  Save this article

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

Author

Listed:
  • Alfonsi Aurélien

    (e-mail : alfonsi@cermics.enpc.fr)

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
    as

    Download full text from publisher

    File URL: https://doi.org/10.1515/156939605777438569
    Download Restriction: For access to full text, subscription to the journal or payment for the individual article is required.
    File URL: https://libkey.io/10.1515/156939605777438569?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to

    for a different version of it.

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    2. 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.
    3. Andreas Neuenkirch & Lukasz Szpruch, 2012. "First order strong approximations of scalar SDEs with values in a domain," Papers 1209.0390, arXiv.org.
    4. 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.
    5. 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.
    6. 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.
    7. repec:hal:wpaper:hal-00768571 is not listed on IDEAS
    8. Ke Du & Eckhard Platen & Renata Rendek, 2012. "Modeling of Oil Prices," Research Paper Series 321, Quantitative Finance Research Centre, University of Technology, Sydney.
    9. 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.
    10. repec:dau:papers:123456789/7818 is not listed on IDEAS
    11. Timothée Papin & Gabriel Turinici, 2014. "Prepayment option of a perpetual corporate loan: the impact of the funding costs," Post-Print hal-00768571, HAL.
    12. 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.
    13. 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.
    14. 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.
    15. Benjamin Jourdain & Mohamed Sbai, 2013. "High order discretization schemes for stochastic volatility models," Post-Print hal-00409861, HAL.
    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. 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.
    18. 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.
    19. Eckhard Platen & Renata Rendek, 2012. "The Affine Nature of Aggregate Wealth Dynamics," Research Paper Series 322, Quantitative Finance Research Centre, University of Technology, Sydney.
    20. Timothée Papin & Gabriel Turinici, 2013. "Valuation of the Prepayment Option of a Perpetual Corporate Loan," Post-Print hal-00653041, HAL.
    21. 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.
    22. 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.
    23. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Rehez Ahlip & Laurence A. F. Park & Ante Prodan, 2017. "Pricing currency options in the Heston/CIR double exponential jump-diffusion model," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 4(01), pages 1-30, March.
    2. Cheikh Mbaye & Frédéric Vrins, 2022. "Affine term structure models: A time‐change approach with perfect fit to market curves," Mathematical Finance, Wiley Blackwell, vol. 32(2), pages 678-724, April.
    3. Dassios, Angelos & Lim, Jia Wei & Qu, Yan, 2020. "Azéma martingales for Bessel and CIR processes and the pricing of Parisian zero-coupon bonds," LSE Research Online Documents on Economics 101765, London School of Economics and Political Science, LSE Library.
    4. El Kolei, Salima & Pelgrin, Florian, 2017. "Parametric inference of autoregressive heteroscedastic models with errors in variables," Statistics & Probability Letters, Elsevier, vol. 130(C), pages 63-70.
    5. Angelos Dassios & Jia Wei Lim & Yan Qu, 2020. "Azéma martingales for Bessel and CIR processes and the pricing of Parisian zero‐coupon bonds," Mathematical Finance, Wiley Blackwell, vol. 30(4), pages 1497-1526, October.
    6. Guo, Zhi Jun, 2008. "A note on the CIR process and the existence of equivalent martingale measures," Statistics & Probability Letters, Elsevier, vol. 78(5), pages 481-487, April.
    7. Christoph Reisinger & Maria Olympia Tsianni, 2025. "Numerical analysis of a particle system for the calibrated Heston-type local stochastic volatility model," Papers 2504.14343, arXiv.org.
    8. repec:hal:wpaper:hal-03827332 is not listed on IDEAS
    9. Thomas Kokholm & Martin Stisen, 2015. "Joint pricing of VIX and SPX options with stochastic volatility and jump models," Journal of Risk Finance, Emerald Group Publishing Limited, vol. 16(1), pages 27-48, January.
    10. Darren Shannon & Grigorios Fountas, 2021. "Extending the Heston Model to Forecast Motor Vehicle Collision Rates," Papers 2104.11461, arXiv.org, revised May 2021.
    11. Chang, Chuang-Chang & Hsieh, Pei-Fang & Tang, Chih-Wei & Wang, Yaw-Huei, 2013. "The intraday behavior of information misreaction across various categories of investors in the Taiwan options market," Journal of Financial Markets, Elsevier, vol. 16(2), pages 362-385.
    12. Choi, Jaehyuk & Kwok, Yue Kuen, 2024. "Simulation schemes for the Heston model with Poisson conditioning," European Journal of Operational Research, Elsevier, vol. 314(1), pages 363-376.
    13. Tore Selland Kleppe & Jun Yu & H.J. Skaug, 2010. "Simulated maximum likelihood estimation of continuous time stochastic volatility models," Advances in Econometrics, in: Maximum Simulated Likelihood Methods and Applications, pages 137-161, Emerald Group Publishing Limited.
    14. A. Itkin & V. Shcherbakov & A. Veygman, 2019. "New Model For Pricing Quanto Credit Default Swaps," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 22(03), pages 1-37, May.
    15. Dotsis, George & Psychoyios, Dimitris & Skiadopoulos, George, 2007. "An empirical comparison of continuous-time models of implied volatility indices," Journal of Banking & Finance, Elsevier, vol. 31(12), pages 3584-3603, December.
    16. Yang, Nian & Chen, Nan & Wan, Xiangwei, 2019. "A new delta expansion for multivariate diffusions via the Itô-Taylor expansion," Journal of Econometrics, Elsevier, vol. 209(2), pages 256-288.
    17. Almeida, Thiago Ramos, 2024. "Estimating time-varying factors’ variance in the string-term structure model with stochastic volatility," Research in International Business and Finance, Elsevier, vol. 70(PA).
    18. Giandomenico, Rossano, 2015. "Financial Methods: A Quantitative Approach," MPRA Paper 71919, University Library of Munich, Germany.
    19. Chenxu Li, 2014. "Closed-Form Expansion, Conditional Expectation, and Option Valuation," Mathematics of Operations Research, INFORMS, vol. 39(2), pages 487-516, May.
    20. Levendorskii, Sergei, 2004. "Consistency conditions for affine term structure models," Stochastic Processes and their Applications, Elsevier, vol. 109(2), pages 225-261, February.
    21. O. Samimi & Z. Mardani & S. Sharafpour & F. Mehrdoust, 2017. "LSM Algorithm for Pricing American Option Under Heston–Hull–White’s Stochastic Volatility Model," Computational Economics, Springer;Society for Computational Economics, vol. 50(2), pages 173-187, August.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:bpj:mcmeap:v:11:y:2005:i:4:p:355-384:n:5. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Peter Golla (email available below). General contact details of provider: https://www.degruyterbrill.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.