IDEAS home Printed from
MyIDEAS: Log in (now much improved!) to save this paper

Equivalence of interest rate models and lattice gases

Listed author(s):
  • Dan Pirjol
Registered author(s):

    We consider the class of short rate interest rate models for which the short rate is proportional to the exponential of a Gaussian Markov process x(t) in the terminal measure r(t) = a(t) exp(x(t)). These models include the Black, Derman, Toy and Black, Karasinski models in the terminal measure. We show that such interest rate models are equivalent with lattice gases with attractive two-body interaction V(t1,t2)= -Cov(x(t1),x(t2)). We consider in some detail the Black, Karasinski model with x(t) an Ornstein, Uhlenbeck process, and show that it is similar with a lattice gas model considered by Kac and Helfand, with attractive long-range two-body interactions V(x,y) = -\alpha (e^{-\gamma |x - y|} - e^{-\gamma (x + y)}). An explicit solution for the model is given as a sum over the states of the lattice gas, which is used to show that the model has a phase transition similar to that found previously in the Black, Derman, Toy model in the terminal measure.

    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:
    File Function: Latest version
    Download Restriction: no

    Paper provided by in its series Papers with number 1204.0915.

    in new window

    Date of creation: Apr 2012
    Handle: RePEc:arx:papers:1204.0915
    Contact details of provider: Web page:

    No references listed on IDEAS
    You can help add them by filling out this form.

    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:arx:papers:1204.0915. 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)

    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.