IDEAS home Printed from https://ideas.repec.org/a/wsi/ijtafx/v11y2008i01ns0219024908004725.html
   My bibliography  Save this article

The Least Cost Super Replicating Portfolio In The Boyle–Vorst Model With Transaction Costs

Author

Listed:
  • GUAN-YU CHEN

    (Department of Mathematics, Cornell University, Ithaca, New York, USA)

  • KEN PALMER

    (Department of Mathematics, and Taida Institute for Mathematical Sciences, National Taiwan University, Taipei 10617, Taiwan)

  • YUAN-CHUNG SHEU

    (Department of Applied Mathematics, National Chiao Tung University, Hsinchu 30050, Taiwan)

Abstract

Boyle and Vorst work in the framework of the binomial model and derive self-financing strategies perfectly replicating the final payoffs to long and short positions in call and put options, assuming proportional transactions costs on trades in the stock and no transactions costs on trades in the bond. Even when the market is arbitrage-free and a given contingent claim has a unique replicating portfolio, there may exist super replicating portfolios of lower cost. Bensaid et al. gave conditions under which the cost of the replicating portfolio does not exceed the cost of any super replicating portfolio. These results were generalized by Stettner, Rutkowski and Palmer to the case of asymmetric transaction costs.In this paper, we first determine the number of replicating portfolios and then compute the least cost super replicating portfolio for any contingent claim in a one-period binomial model. By using the fundamental theorem of linear programming, we show that there are only finitely many possibilities for a least cost super replicating portfolio for any contingent claim in a two-period binomial model. As an application of our results, we give an example in which we compute the least cost super replicating portfolio for a butterfly spread in a two-period model.

Suggested Citation

  • Guan-Yu Chen & Ken Palmer & Yuan-Chung Sheu, 2008. "The Least Cost Super Replicating Portfolio In The Boyle–Vorst Model With Transaction Costs," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 11(01), pages 55-85.
    • Handle: RePEc:wsi:ijtafx:v:11:y:2008:i:01:n:s0219024908004725
    DOI: 10.1142/S0219024908004725
    as

    Download full text from publisher

    File URL: http://www.worldscientific.com/doi/abs/10.1142/S0219024908004725
    Download Restriction: Access to full text is restricted to subscribers
    File URL: https://libkey.io/10.1142/S0219024908004725?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.

    Citations

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


    Cited by:

    1. Yuan Hu & Abootaleb Shirvani & W. Brent Lindquist & Frank J. Fabozzi & Svetlozar T. Rachev, 2021. "Market Complete Option Valuation using a Jarrow-Rudd Pricing Tree with Skewness and Kurtosis," Papers 2106.09128, arXiv.org.
    2. Alet Roux & Tomasz Zastawniak, 2016. "Game options with gradual exercise and cancellation under proportional transaction costs," Papers 1612.02312, arXiv.org.
    3. Hu, Yuan & Lindquist, W. Brent & Rachev, Svetlozar T. & Shirvani, Abootaleb & Fabozzi, Frank J., 2022. "Market complete option valuation using a Jarrow-Rudd pricing tree with skewness and kurtosis," Journal of Economic Dynamics and Control, Elsevier, vol. 137(C).

    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:11:y:2008:i:01:n:s0219024908004725. 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.

    We have no bibliographic references for this item. You can help adding them by using 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.