IDEAS home Printed from
   My bibliography  Save this paper

A unified view of LIBOR models


  • Kathrin Glau
  • Zorana Grbac
  • Antonis Papapantoleon


We provide a unified framework for modeling LIBOR rates using general semimartingales as driving processes and generic functional forms to describe the evolution of the dynamics. We derive sufficient conditions for the model to be arbitrage-free which are easily verifiable, and for the LIBOR rates to be true martingales under the respective forward measures. We discuss when the conditions are also necessary and comment on further desirable properties such as those leading to analytical tractability and positivity of rates. This framework allows to consider several popular models in the literature, such as LIBOR market models driven by Brownian motion or jump processes, the L\'evy forward price model as well as the affine LIBOR model, under one umbrella. Moreover, we derive structural results about LIBOR models and show, in particular, that only models where the forward price is an exponentially affine function of the driving process preserve their structure under different forward measures.

Suggested Citation

  • Kathrin Glau & Zorana Grbac & Antonis Papapantoleon, 2016. "A unified view of LIBOR models," Papers 1601.01352,, revised Jul 2016.
  • Handle: RePEc:arx:papers:1601.01352

    Download full text from publisher

    File URL:
    File Function: Latest version
    Download Restriction: no

    References listed on IDEAS

    1. Alan Brace & Dariusz G¬łatarek & Marek Musiela, 1997. "The Market Model of Interest Rate Dynamics," Mathematical Finance, Wiley Blackwell, vol. 7(2), pages 127-155.
    2. Antonis Papapantoleon, 2009. "Old and new approaches to LIBOR modeling," Papers 0910.4941,, revised Apr 2010.
    3. Farshid Jamshidian, 1997. "LIBOR and swap market models and measures (*)," Finance and Stochastics, Springer, vol. 1(4), pages 293-330.
    4. Miltersen, Kristian R & Sandmann, Klaus & Sondermann, Dieter, 1997. " Closed Form Solutions for Term Structure Derivatives with Log-Normal Interest Rates," Journal of Finance, American Finance Association, vol. 52(1), pages 409-430, March.
    5. David Criens & Kathrin Glau & Zorana Grbac, 2015. "Martingale property of exponential semimartingales: a note on explicit conditions and applications to financial models," Papers 1506.08127,, revised Aug 2016.
    6. Wolfgang Kluge & Antonis Papapantoleon, 2009. "On the valuation of compositions in L\'evy term structure models," Papers 0902.3456,
    7. Marek Rutkowski & Marek Musiela, 1997. "Continuous-time term structure models: Forward measure approach (*)," Finance and Stochastics, Springer, vol. 1(4), pages 261-291.
    8. Goll, Thomas & Kallsen, Jan, 2000. "Optimal portfolios for logarithmic utility," Stochastic Processes and their Applications, Elsevier, vol. 89(1), pages 31-48, September.
    9. Antonis Papapantoleon, 2010. "Old and new approaches to LIBOR modeling," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 64(s1), pages 257-275.
    10. Wolfgang Kluge & Antonis Papapantoleon, 2009. "On the valuation of compositions in Levy term structure models," Quantitative Finance, Taylor & Francis Journals, vol. 9(8), pages 951-959.
    Full references (including those not matched with items on IDEAS)

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:


    Access and download statistics


    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:arx:papers:1601.01352. 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: (arXiv administrators). General contact details of provider: .

    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 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.

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.