IDEAS home Printed from https://ideas.repec.org/
MyIDEAS: Log in (now much improved!) to save this paper

Approximate Option Pricing in the L\'evy Libor Model

Listed author(s):
  • Zorana Grbac
  • David Krief
  • Peter Tankov

In this paper we consider the pricing of options on interest rates such as caplets and swaptions in the L\'evy Libor model developed by Eberlein and \"Ozkan (2005). This model is an extension to L\'evy driving processes of the classical log-normal Libor market model (LMM) driven by a Brownian motion. Option pricing is significantly less tractable in this model than in the LMM due to the appearance of stochastic terms in the jump part of the driving process when performing the measure changes which are standard in pricing of interest rate derivatives. To obtain explicit approximation for option prices, we propose to treat a given L\'evy Libor model as a suitable perturbation of the log-normal LMM. The method is inspired by recent works by Cern\'y, Denkl and Kallsen (2013) and M\'enass\'e and Tankov (2015). The approximate option prices in the L\'evy Libor model are given as the corresponding LMM prices plus correction terms which depend on the characteristics of the underlying L\'evy process and some additional terms obtained from the LMM model.

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://arxiv.org/pdf/1511.08466
File Function: Latest version
Download Restriction: no

Paper provided by arXiv.org in its series Papers with number 1511.08466.

as
in new window

Length:
Date of creation: Nov 2015
Date of revision: Jul 2016
Handle: RePEc:arx:papers:1511.08466
Contact details of provider: Web page: http://arxiv.org/

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. Alan Brace & Dariusz G¸atarek & Marek Musiela, 1997. "The Market Model of Interest Rate Dynamics," Mathematical Finance, Wiley Blackwell, vol. 7(2), pages 127-155.
  2. 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.
  3. repec:dau:papers:123456789/1380 is not listed on IDEAS
  4. Peter Carr & Hélyette Geman & Dilip B. Madan & Marc Yor, 2007. "Self-Decomposability And Option Pricing," Mathematical Finance, Wiley Blackwell, vol. 17(1), pages 31-57.
  5. Ale\v{s} \v{C}ern\'y & Stephan Denkl & Jan Kallsen, 2013. "Hedging in L\'evy Models and the Time Step Equivalent of Jumps," Papers 1309.7833, arXiv.org, revised Jul 2017.
  6. Antonis Papapantoleon & John Schoenmakers & David Skovmand, 2011. "Efficient and accurate log-L\'evy approximations to L\'evy driven LIBOR models," Papers 1106.0866, arXiv.org, revised Jan 2012.
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:arx:papers:1511.08466. 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.