IDEAS home Printed from https://ideas.repec.org/
MyIDEAS: Login to save this paper or follow this series

Sufficient and necessary conditions for perpetual multi-assets exchange options

  • GAHUNGU, Joachim

    ()

    (Université catholique de Louvain, CORE, B-1348 Louvain-la-Neuve, Belgium)

  • SMEERS, Yves

    ()

    (Université catholique de Louvain, CORE, B-1348 Louvain-la-Neuve, Belgium)

Registered author(s):

    This paper considers the general problem of optimal timing of the exchange of the sum of n Ito-diffusions for the sum of m others (e.g., the optimal time to exchange a geometric Brownian motion for a geometric mean reverting process). We first contribute to the literature by providing analytical sufficient conditions and necessary conditions for optimal stopping (i.e. sub- and super- sets of the stopping region) for some sub-cases of the general problem. We then exhibit a connection between the problem of finding sufficient conditions for optimal stopping and linear programming. This connection provides a unified approach which does not only allow to recover previous analytically determinable subsets of the stopping region, but also allows to characterize (more complex) subsets of the stopping region that do not have an analytical expression. In the particular case where all assets are geometric Brownian motions, this connection gives us new insights. In particular, it simplifies the expression of the subset of the stopping region identified by Nishide and Rogers (2011). Our numerical examples finally confirms the good behavior of the candidate investment rule introduced by Gahungu and Smeers (2011) for this particular case, which seems to comfort a conjecture that their rule might be optimal.

    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://uclouvain.be/cps/ucl/doc/core/documents/coredp2011_35web.pdf
    Download Restriction: no

    Paper provided by Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) in its series CORE Discussion Papers with number 2011035.

    as
    in new window

    Length:
    Date of creation: 01 Jul 2011
    Date of revision:
    Handle: RePEc:cor:louvco:2011035
    Contact details of provider: Postal: Voie du Roman Pays 34, 1348 Louvain-la-Neuve (Belgium)
    Phone: 32(10)474321
    Fax: +32 10474304
    Web page: http://www.uclouvain.be/core
    Email:


    More information through EDIRC

    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. Yaozhong Hu & Bernt Øksendal, 1998. "Optimal time to invest when the price processes are geometric Brownian motions," Finance and Stochastics, Springer, vol. 2(3), pages 295-310.
    2. Gilbert E. Metcalf & Kevin A. Hassett, 1995. "Investment Under Alternative Return Assumptions: Comparing Random Walks and Mean Reversion," NBER Technical Working Papers 0175, National Bureau of Economic Research, Inc.
    3. Svetlana Boyarchenko & Sergey Levendorskiy, 2004. "Optimal stopping made easy," Finance 0410016, EconWPA.
    4. McDonald, Robert & Siegel, Daniel, 1986. "The Value of Waiting to Invest," The Quarterly Journal of Economics, MIT Press, vol. 101(4), pages 707-27, November.
    5. Duranton, Gilles & Martin, Philippe & Mayer, Thierry & Mayneris, Florian, 2010. "The Economics of Clusters: Lessons from the French Experience," OUP Catalogue, Oxford University Press, number 9780199592203, March.
    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:cor:louvco:2011035. 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: (Alain GILLIS)

    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.