IDEAS home Printed from https://ideas.repec.org/
MyIDEAS: Login to save this article or follow this journal

On arbitrage and Markovian short rates in fractional bond markets

  • Gapeev, Pavel V.
Registered author(s):

    We study a bond market model and related term structure of interest rates driven by a fractional Brownian motion with self-similarity parameter H[set membership, variant](1/2,1). We present a criterion on the deterministic forward rate volatility under which the short rate process is Markovian and construct an admissible self-financing portfolio realizing an arbitrage opportunity.

    If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.

    File URL: http://www.sciencedirect.com/science/article/B6V1D-4DR1G43-3/2/679277a7f6dc8da32b08d3a8c681aa2b
    Download Restriction: Full text for ScienceDirect subscribers only

    As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.

    Article provided by Elsevier in its journal Statistics & Probability Letters.

    Volume (Year): 70 (2004)
    Issue (Month): 3 (December)
    Pages: 211-222

    as
    in new window

    Handle: RePEc:eee:stapro:v:70:y:2004:i:3:p:211-222
    Contact details of provider: Web page: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description

    Order Information: Postal: http://www.elsevier.com/wps/find/supportfaq.cws_home/regional
    Web: https://shop.elsevier.com/order?id=505573&ref=505573_01_ooc_1&version=01

    References listed on IDEAS
    Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:

    as in new window
    1. Björk, Tomas & di Masi, Giovanni & Kabanov, Yuri & Runggaldier, Wolfgang, 1996. "Towards a General Theory of Bond Markets," SSE/EFI Working Paper Series in Economics and Finance 143, Stockholm School of Economics.
    2. L. C. G. Rogers, 1997. "Arbitrage with Fractional Brownian Motion," Mathematical Finance, Wiley Blackwell, vol. 7(1), pages 95-105.
    3. Salopek, D. M., 1998. "Tolerance to arbitrage," Stochastic Processes and their Applications, Elsevier, vol. 76(2), pages 217-230, August.
    4. Tommi Sottinen, 2001. "Fractional Brownian motion, random walks and binary market models," Finance and Stochastics, Springer, vol. 5(3), pages 343-355.
    5. Tomas Björk & Yuri Kabanov & Wolfgang Runggaldier, 1997. "Bond Market Structure in the Presence of Marked Point Processes," Mathematical Finance, Wiley Blackwell, vol. 7(2), pages 211-239.
    6. Andrew Carverhill, 1994. "When Is The Short Rate Markovian?," Mathematical Finance, Wiley Blackwell, vol. 4(4), pages 305-312.
    7. Heath, David & Jarrow, Robert & Morton, Andrew, 1992. "Bond Pricing and the Term Structure of Interest Rates: A New Methodology for Contingent Claims Valuation," Econometrica, Econometric Society, vol. 60(1), pages 77-105, January.
    8. Gapeev, Pavel V. & Küchler, Uwe, 2003. "On Markovian Short Rates in Term Structure Models Driven by Jump-Diffusion Processes," SFB 373 Discussion Papers 2003,44, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    9. Le Breton, Alain, 1998. "Filtering and parameter estimation in a simple linear system driven by a fractional Brownian motion," Statistics & Probability Letters, Elsevier, vol. 38(3), pages 263-274, June.
    10. Rimas Norvaisa, 2000. "Modelling of stock price changes: A real analysis approach," Finance and Stochastics, Springer, vol. 4(3), pages 343-369.
    11. Ernst Eberlein & Sebastian Raible, 1999. "Term Structure Models Driven by General Lévy Processes," Mathematical Finance, Wiley Blackwell, vol. 9(1), pages 31-53.
    12. Küchler, Uwe & Naumann, Eva, 2003. "Markovian short rates in a forward rate model with a general class of Lévy processes," SFB 373 Discussion Papers 2003,6, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    13. Sottinen Tommi & Valkeila Esko, 2003. "On arbitrage and replication in the fractional Black–Scholes pricing model," Statistics & Risk Modeling, De Gruyter, vol. 21(2/2003), pages 93-108, February.
    Full references (including those not matched with items on IDEAS)

    This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

    When requesting a correction, please mention this item's handle: RePEc:eee:stapro:v:70:y:2004:i:3:p:211-222. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Zhang, Lei)

    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 references are entirely missing, you can add them using this form.

    If the full references list an item that is present in RePEc, but the system did not link 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 profile, as there may be some citations waiting for confirmation.

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

    This information is provided to you by IDEAS at the Research Division of the Federal Reserve Bank of St. Louis using RePEc data.