Symmetry and duality in Levy markets
The aim of this paper is to introduce the notion of symmetry in a Levy market. This notion appears as a particular case of a general known relation between prices of put and call options, of both the European and the American type, which is also reviewed in the paper, and that we call put-call duality. Symmetric Levy markets have the distinctive feature of producing symmetric smile curves, in the log of strike/futures prices. Put-call duality is obtained as a consequence of a change of the risk neutral probability measure through Girsanov's theorem, when considering the discounted and reinvested stock price as the numeraire. Symmetry is defined when a certain law before and after the change of measure through Girsanov's theorem coincides. A parameter characterizing the departure from symmetry is introduced, and a necessary and sufficient condition for symmetry to hold is obtained, in terms of the jump measure of the Levy process, answering a question raised by Carr and Chesney (American put call symmetry, preprint, 1996). Some empirical evidence is shown, supporting that, in general, markets are not symmetric.
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.
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.
Volume (Year): 6 (2006)
Issue (Month): 3 ()
|Contact details of provider:|| Web page: http://www.tandfonline.com/RQUF20|
|Order Information:||Web: http://www.tandfonline.com/pricing/journal/RQUF20|
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.:
- José Fajardo & Aquiles Farias, 2002.
"Generalized Hyperbolic Distributions and Brazilian Data,"
Working Papers Series
52, Central Bank of Brazil, Research Department.
- Fajardo, J. & Farias, A., 2003. "Generalized Hyperbolic Distributions and Brazilian Data," Finance Lab Working Papers flwp_57, Finance Lab, Insper Instituto de Ensino e Pesquisa.
- S. G. Kou & Hui Wang, 2004. "Option Pricing Under a Double Exponential Jump Diffusion Model," Management Science, INFORMS, vol. 50(9), pages 1178-1192, September.
- Merton, Robert C., 1976.
"Option pricing when underlying stock returns are discontinuous,"
Journal of Financial Economics,
Elsevier, vol. 3(1-2), pages 125-144.
- Merton, Robert C., 1975. "Option pricing when underlying stock returns are discontinuous," Working papers 787-75., Massachusetts Institute of Technology (MIT), Sloan School of Management.
- Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-54, May-June.
- Orlin Grabbe, J., 1983. "The pricing of call and put options on foreign exchange," Journal of International Money and Finance, Elsevier, vol. 2(3), pages 239-253, December.
- Schroder, Mark, 1999. "Changes of Numeraire for Pricing Futures, Forwards, and Options," Review of Financial Studies, Society for Financial Studies, vol. 12(5), pages 1143-63.
- Peter Carr & Helyette Geman, 2002. "The Fine Structure of Asset Returns: An Empirical Investigation," The Journal of Business, University of Chicago Press, vol. 75(2), pages 305-332, April.
- Eberlein, Ernst & Keller, Ulrich & Prause, Karsten, 1998. "New Insights into Smile, Mispricing, and Value at Risk: The Hyperbolic Model," The Journal of Business, University of Chicago Press, vol. 71(3), pages 371-405, July.
When requesting a correction, please mention this item's handle: RePEc:taf:quantf:v:6:y:2006:i:3:p:219-227. 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: (Michael McNulty)
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.