IDEAS home Printed from https://ideas.repec.org/p/pra/mprapa/42094.html
   My bibliography  Save this paper

Arbitrarily Fast CRR Schemes

Author

Listed:
  • Leduc, Guillaume

Abstract

We introduce a method for the approximation of a lognormal stock price process by a Cox, Ross and Rubinstein (CRR) type of binomial scheme, which allows to reach arbitrary speed of convergence of order O(n^{-(N/2)}), for any integer N>0.

Suggested Citation

  • Leduc, Guillaume, 2012. "Arbitrarily Fast CRR Schemes," MPRA Paper 42094, University Library of Munich, Germany, revised 20 Oct 2012.
    • Handle: RePEc:pra:mprapa:42094
    as

    Download full text from publisher

    File URL: https://mpra.ub.uni-muenchen.de/42094/1/MPRA_paper_42094.pdf
    File Function: original version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Lo-Bin Chang & Ken Palmer, 2007. "Smooth convergence in the binomial model," Finance and Stochastics, Springer, vol. 11(1), pages 91-105, January.
    2. Francine Diener & MARC Diener, 2004. "Asymptotics of the price oscillations of a European call option in a tree model," Mathematical Finance, Wiley Blackwell, vol. 14(2), pages 271-293, April.
    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. Alona Bock & Ralf Korn, 2016. "Improving Convergence of Binomial Schemes and the Edgeworth Expansion," Risks, MDPI, vol. 4(2), pages 1-22, May.

    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. Alona Bock & Ralf Korn, 2016. "Improving Convergence of Binomial Schemes and the Edgeworth Expansion," Risks, MDPI, vol. 4(2), pages 1-22, May.
    2. Ratibenyakool, Yuttana & Neammanee, Kritsana, 2024. "Rate of convergence of trinomial formula to Black–Scholes formula," Statistics & Probability Letters, Elsevier, vol. 213(C).
    3. Karl Grosse-Erdmann & Fabien Heuwelyckx, 2015. "The pricing of lookback options and binomial approximation," Papers 1502.02819, arXiv.org.
    4. Ralf Korn & Stefanie Müller, 2013. "The optimal-drift model: an accelerated binomial scheme," Finance and Stochastics, Springer, vol. 17(1), pages 135-160, January.
    5. Fabien Heuwelyckx, 2013. "Convergence of European Lookback Options with Floating Strike in the Binomial Model," Papers 1302.2312, arXiv.org, revised Oct 2013.
    6. Jean-Christophe Breton & Youssef El-Khatib & Jun Fan & Nicolas Privault, 2021. "A q-binomial extension of the CRR asset pricing model," Papers 2104.10163, arXiv.org, revised Feb 2023.
    7. Guillaume Leduc & Merima Nurkanovic Hot, 2020. "Joshi’s Split Tree for Option Pricing," Risks, MDPI, vol. 8(3), pages 1-26, August.
    8. Elisa Appolloni & Andrea Ligori, 2014. "Efficient tree methods for pricing digital barrier options," Papers 1401.2900, arXiv.org, revised Jan 2014.
    9. Gongqiu Zhang & Lingfei Li, 2019. "Analysis of Markov Chain Approximation for Option Pricing and Hedging: Grid Design and Convergence Behavior," Operations Research, INFORMS, vol. 67(2), pages 407-427, March.
    10. Karl Grosse-Erdmann & Fabien Heuwelyckx, 2016. "The pricing of lookback options and binomial approximation," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 39(1), pages 33-67, April.
    11. San-Lin Chung & Pai-Ta Shih, 2007. "Generalized Cox-Ross-Rubinstein Binomial Models," Management Science, INFORMS, vol. 53(3), pages 508-520, March.
    12. Wael Bahsoun & Pawel Góra & Silvia Mayoral & Manuel Morales, 2006. "Random Dynamics and Finance: Constructing Implied Binomial Trees from a Predetermined Stationary Den," Faculty Working Papers 13/06, School of Economics and Business Administration, University of Navarra.
    13. Glazyrina, Anna & Melnikov, Alexander, 2016. "Bernstein’s inequalities and their extensions for getting the Black–Scholes option pricing formula," Statistics & Probability Letters, Elsevier, vol. 111(C), pages 86-92.
    14. Mark Joshi & Mike Staunton, 2012. "On the analytical/numerical pricing of American put options against binomial tree prices," Quantitative Finance, Taylor & Francis Journals, vol. 12(1), pages 17-20, December.
    15. Guillaume Leduc, 2025. "Convergence Speed of Bermudan, Randomized Bermudan, and Canadian Options," Mathematics, MDPI, vol. 13(2), pages 1-14, January.
    16. Ghafarian, Bahareh & Hanafizadeh, Payam & Qahi, Amir Hossein Mortazavi, 2018. "Applying Greek letters to robust option price modeling by binomial-tree," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 503(C), pages 632-639.
    17. Atul Chandra & Peter R. Hartley & Gopalan Nair, 2022. "Multiple Volatility Real Options Approach to Investment Decisions Under Uncertainty," Decision Analysis, INFORMS, vol. 19(2), pages 79-98, June.
    18. Mark Joshi, 2009. "Achieving smooth asymptotics for the prices of European options in binomial trees," Quantitative Finance, Taylor & Francis Journals, vol. 9(2), pages 171-176.
    19. Kyoung-Sook Moon & Hongjoong Kim, 2013. "A multi-dimensional local average lattice method for multi-asset models," Quantitative Finance, Taylor & Francis Journals, vol. 13(6), pages 873-884, May.
    20. N. El Karoui & Y. Jiao, 2009. "Stein’s method and zero bias transformation for CDO tranche pricing," Finance and Stochastics, Springer, vol. 13(2), pages 151-180, April.

    More about this item

    Keywords

    European options; binomial scheme error; Black-Scholes;
    All these keywords.

    JEL classification:

    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

    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:pra:mprapa:42094. 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: Joachim Winter (email available below). General contact details of provider: https://edirc.repec.org/data/vfmunde.html .

    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.