IDEAS home Printed from https://ideas.repec.org/a/wsi/ijtafx/v17y2014i04ns0219024914500253.html
   My bibliography  Save this article

Convergence Of European Lookback Options With Floating Strike In The Binomial Model

Author

Listed:
  • FABIEN HEUWELYCKX

    (Institut Complexys, Département de Mathématique, Université de Mons, 20 Place du Parc, 7000 Mons, Belgium)

Abstract

In this paper, we study the convergence of a European lookback option with floating strike evaluated with the binomial model of Cox–Ross–Rubinstein to its evaluation with the Black–Scholes model. We do the same for its delta. We confirm that these convergences are of order $1/\sqrt{n}$. For this, we use the binomial model of Cheuk–Vorst which allows us to write the price of the option using a double sum. Based on an improvement of a lemma of Lin–Palmer, we are able to give the precise value of the term in $1/\sqrt{n}$ in the expansion of the error; we also obtain the value of the term in 1/n if the risk free interest rate is nonzero. This modelization will also allow us to determine the first term in the expansion of the delta.

Suggested Citation

  • Fabien Heuwelyckx, 2014. "Convergence Of European Lookback Options With Floating Strike In The Binomial Model," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 17(04), pages 1-24.
    • Handle: RePEc:wsi:ijtafx:v:17:y:2014:i:04:n:s0219024914500253
    DOI: 10.1142/S0219024914500253
    as

    Download full text from publisher

    File URL: http://www.worldscientific.com/doi/abs/10.1142/S0219024914500253
    Download Restriction: Access to full text is restricted to subscribers
    File URL: https://libkey.io/10.1142/S0219024914500253?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 search for a different version of it.

    References listed on IDEAS

    as
    1. Lyuu,Yuh-Dauh, 2002. "Financial Engineering and Computation," Cambridge Books, Cambridge University Press, number 9780521781718.
    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. Karl Grosse-Erdmann & Fabien Heuwelyckx, 2015. "The pricing of lookback options and binomial approximation," Papers 1502.02819, arXiv.org.
    2. Deng, Guohe, 2020. "Pricing perpetual American floating strike lookback option under multiscale stochastic volatility model," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).
    3. Guillaume Leduc & Merima Nurkanovic Hot, 2020. "Joshi’s Split Tree for Option Pricing," Risks, MDPI, vol. 8(3), pages 1-26, August.
    4. 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.

    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. Yuh-Dauh Lyuu & Cheng-Wei Wu, 2010. "An improved combinatorial approach for pricing Parisian options," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 33(1), pages 49-61, May.
    2. Kyoung-Sook Moon & Yunju Jeong & Hongjoong Kim, 2016. "An Efficient Binomial Method for Pricing Asian Options," ECONOMIC COMPUTATION AND ECONOMIC CYBERNETICS STUDIES AND RESEARCH, Faculty of Economic Cybernetics, Statistics and Informatics, vol. 50(2), pages 151-164.
    3. R. Vilela Mendes, 2022. "The fractional volatility model and rough volatility," Papers 2206.02205, arXiv.org.
    4. Forster, Martin & La Torre, Davide & Lambert, Peter J., 2014. "Optimal control of inequality under uncertainty," Mathematical Social Sciences, Elsevier, vol. 68(C), pages 53-59.
    5. U Hou Lok & Yuh‐Dauh Lyuu, 2020. "Efficient trinomial trees for local‐volatility models in pricing double‐barrier options," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 40(4), pages 556-574, April.
    6. Da-Rocha, José-María & Restuccia, Diego & Tavares, Marina M., 2023. "Policy distortions and aggregate productivity with endogenous establishment-level productivity," European Economic Review, Elsevier, vol. 155(C).
    7. Hidetoshi Nakagawa & Tomoaki Shouda, 2004. "Analyses of Mortgage-Backed Securities Based on Unobservable Prepayment Cost Processes," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 11(3), pages 233-266, September.
    8. Tian-Shyr Dai, 2009. "Efficient option pricing on stocks paying discrete or path-dependent dividends with the stair tree," Quantitative Finance, Taylor & Francis Journals, vol. 9(7), pages 827-838.
    9. Dai, Tian-Shyr & Yang, Sharon S. & Liu, Liang-Chih, 2015. "Pricing guaranteed minimum/lifetime withdrawal benefits with various provisions under investment, interest rate and mortality risks," Insurance: Mathematics and Economics, Elsevier, vol. 64(C), pages 364-379.
    10. Teselios, Delia & Albici, Mihaela, 2009. "On financial derivatives and differential equations used in their assessment," MPRA Paper 18225, University Library of Munich, Germany.
    11. Wang Xiaodong, 2007. "The Closed-form Solution for Pricing American Put Options," Annals of Economics and Finance, Society for AEF, vol. 8(1), pages 197-215, May.
    12. U Hou Lok & Yuh-Dauh Lyuu, 2022. "A Valid and Efficient Trinomial Tree for General Local-Volatility Models," Computational Economics, Springer;Society for Computational Economics, vol. 60(3), pages 817-832, October.
    13. Tian-Shyr Dai & Yuh-Dauh Lyuu, 2002. "Efficient, exact algorithms for asian options with multiresolution lattices," Review of Derivatives Research, Springer, vol. 5(2), pages 181-203, May.

    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:wsi:ijtafx:v:17:y:2014:i:04:n:s0219024914500253. 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: Tai Tone Lim (email available below). General contact details of provider: http://www.worldscinet.com/ijtaf/ijtaf.shtml .

    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.