Advanced Search
MyIDEAS: Login

Implied Binomial Trees

Contents:

Author Info

  • Mark Rubinstein.
Registered author(s):

    Abstract

    Despite its success, the Black-Scholes formula has become increasingly unreliable over time in the very markets where one would expect it to be most accurate. In addition, attempts by financial economists to extract probabilistic information from option prices have been puny in comparison to what is clearly possible. This paper develops a new method for inferring risk-neutral probabilities (or state- contingent prices) from the simultaneously observed prices of European options. These probabilities are then used to infer a unique fully specified recombining binomial tree that is consistent with these probabilities (and hence consistent with all the observed option prices). If specified exogenously, the model can also accommodate local interest rates and underlying asset payout rates which are general functions of the concurrent underlying asset price and time. In a 200 step lattice, for example, there are a total of 60,301 unknowns: 40,200 potentially different move sizes, 20,100 potentially different move probabilities, and 1 interest rate to be determined from 60,301 independent equations, many of which are non-linear in the unknowns. Despite this, a backwards recursive solution procedure exists which is only slightly more time-consuming than for a standard binomial tree with given constant move sizes and move probabilities. Moreover, closed-form expressions exist for the values and hedging parameters of European options maturing with or before the end of the tree. The tree can also be used to value and hedge American and several types of exotic options. Interpreted in terms of continuous-time diffusion processes, the model here assumes that the drift and local volatility are at most functions of the underlying asset price and time. But instead of beginning with a parameterization of these functions (as in previous research), the model derives these functions endogenously to fit current option prices. As a result, it can be thought of as an attempt to exhaust the potential for single state-variable path-independent diffusion processes to rectify problems with the Black- Scholes formula that arise in practice.

    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: http://www.jstor.org/
    File Function: link to document
    Download Restriction: no

    Bibliographic Info

    Paper provided by University of California at Berkeley in its series Research Program in Finance Working Papers with number RPF-232.

    as in new window
    Length:
    Date of creation: 01 Jan 1994
    Date of revision:
    Handle: RePEc:ucb:calbrf:rpf-232

    Contact details of provider:
    Postal: University of California at Berkeley, Berkeley, CA USA
    Phone: 510-642-0822
    Fax: 510-642-6615
    Email:
    Web page: http://haas.berkeley.edu/finance/WP/rpflist.html
    More information through EDIRC

    Order Information:
    Postal: IBER, F502 Haas Building, University of California at Berkeley, Berkeley CA 94720-1922
    Email:

    Related research

    Keywords:

    This paper has been announced in the following NEP Reports:

    References

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

    Citations

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

    Cited by:
    This item has more than 25 citations. To prevent cluttering this page, these citations are listed on a separate page.

    Lists

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

    Statistics

    Access and download statistics

    Corrections

    When requesting a correction, please mention this item's handle: RePEc:ucb:calbrf:rpf-232. 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: (Christopher F. Baum).

    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.