Advanced Search
MyIDEAS: Login

A Simple Option Formula for General Jump-Diffusion and other Exponential Levy Processes


Author Info

Registered author(s):


    Option values are well-known to be the integral of a discounted transition density times a payoff function; this is just martingale pricing. It's usually done in 'S-space', where S is the terminal security price. But, for Levy processes the S-space transition densities are often very complicated, involving many special functions and infinite summations. Instead, we show that it's much easier to compute the option value as an integral in Fourier space - and interpret this as a Parseval identity. The formula is especially simple because (i) it's a single integration for any payoff and (ii) the integrand is typically a compact expressions with just elementary functions. Our approach clarifies and generalizes previous work using characteristic functions and Fourier inversions. For example, we show how the residue calculus leads to several variation formulas, such as a well-known, but less numerically efficient, 'Black-Scholes style' formula for call options. The result applies to any European-style, simple or exotic option (without path-dependence) under any Lévy process with a known characteristic function

    Download Info

    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:
    Download Restriction: no

    Bibliographic Info

    Paper provided by Finance Press in its series Related articles with number explevy.

    as in new window
    Length: 25 pages
    Date of creation: 06 Aug 2001
    Date of revision:
    Handle: RePEc:vsv:svpubs:explevy

    Contact details of provider:
    Phone: (949)720-9614
    Fax: (949)720-9631
    Web page:

    Related research

    Keywords: option pricing; jump-diffusion; Levy processes; Fourier; characteristic function; transforms; residue; call options; discontinuous; jump processes; analytic characteristic; Levy-Khintchine; infinitely divisible; independent increments;

    Find related papers by JEL classification:

    This paper has been announced in the following NEP Reports:


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


    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as in new window

    Cited by:
    1. Olivier Scaillet., 2003. "Linear-Quadratic Jump-Diffusion Modelling with Application to Stochastic Volatility," THEMA Working Papers 2003-29, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
    2. Roger Lord & Christian Kahl, 2006. "Why the Rotation Count Algorithm works," Tinbergen Institute Discussion Papers 06-065/2, Tinbergen Institute.
    3. Noureddine Krichene, 2005. "Subordinated Levy Processes and Applications to Crude Oil Options," IMF Working Papers 05/174, International Monetary Fund.
    4. Marcelo G. Figueroa, 2006. "Pricing Multiple Interruptible-Swing Contracts," Birkbeck Working Papers in Economics and Finance 0606, Birkbeck, Department of Economics, Mathematics & Statistics.


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


    Access and download statistics


    When requesting a correction, please mention this item's handle: RePEc:vsv:svpubs:explevy. 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: (Alan Lewis).

    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.