• Login
    View Item 
    •   Home
    • Research
    • Articles
    • View Item
    •   Home
    • Research
    • Articles
    • View Item
    JavaScript is disabled for your browser. Some features of this site may not work without it.

    Browse

    All of KAUSTCommunitiesIssue DateSubmit DateThis CollectionIssue DateSubmit Date

    My Account

    Login

    Quick Links

    Open Access PolicyORCID LibguideTheses and Dissertations LibguideSubmit an Item

    Statistics

    Display statistics

    Computable error estimates of a finite difference scheme for option pricing in exponential Lévy models

    • CSV
    • RefMan
    • EndNote
    • BibTex
    • RefWorks
    Type
    Article
    Authors
    Kiessling, Jonas
    Tempone, Raul cc
    KAUST Department
    Applied Mathematics and Computational Science Program
    Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
    Date
    2014-05-06
    Online Publication Date
    2014-05-06
    Print Publication Date
    2014-12
    Permanent link to this record
    http://hdl.handle.net/10754/566088
    
    Metadata
    Show full item record
    Abstract
    Option prices in exponential Lévy models solve certain partial integro-differential equations. This work focuses on developing novel, computable error approximations for a finite difference scheme that is suitable for solving such PIDEs. The scheme was introduced in (Cont and Voltchkova, SIAM J. Numer. Anal. 43(4):1596-1626, 2005). The main results of this work are new estimates of the dominating error terms, namely the time and space discretisation errors. In addition, the leading order terms of the error estimates are determined in a form that is more amenable to computations. The payoff is only assumed to satisfy an exponential growth condition, it is not assumed to be Lipschitz continuous as in previous works. If the underlying Lévy process has infinite jump activity, then the jumps smaller than some (Formula presented.) are approximated by diffusion. The resulting diffusion approximation error is also estimated, with leading order term in computable form, as well as the dependence of the time and space discretisation errors on this approximation. Consequently, it is possible to determine how to jointly choose the space and time grid sizes and the cut off parameter (Formula presented.). © 2014 Springer Science+Business Media Dordrecht.
    Citation
    Kiessling, J., & Tempone, R. (2014). Computable error estimates of a finite difference scheme for option pricing in exponential Lévy models. BIT Numerical Mathematics, 54(4), 1023–1065. doi:10.1007/s10543-014-0490-4
    Sponsors
    The authors would like to recognize the support of the PECOS center at ICES, University of Texas at Austin (Project Number 024550, Center for Predictive Computational Science). Support from the VR project "Effektiva numeriska metoder for stokastiska differentialekvationer med tillampningar" and King Abdullah University of Science and Technology (KAUST) is also acknowledged. The research has also been supported by the Swedish Foundation for Strategic Research (SSF) via the Center for Industrial and Applied Mathematics (CIAM) at KTH. The second author is a member of the KAUST SRI center for Uncertainty Quantification.
    Publisher
    Springer Nature
    Journal
    BIT Numerical Mathematics
    DOI
    10.1007/s10543-014-0490-4
    ae974a485f413a2113503eed53cd6c53
    10.1007/s10543-014-0490-4
    Scopus Count
    Collections
    Articles; Applied Mathematics and Computational Science Program; Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division

    entitlement

     
    DSpace software copyright © 2002-2023  DuraSpace
    Quick Guide | Contact Us | KAUST University Library
    Open Repository is a service hosted by 
    Atmire NV
     

    Export search results

    The export option will allow you to export the current search results of the entered query to a file. Different formats are available for download. To export the items, click on the button corresponding with the preferred download format.

    By default, clicking on the export buttons will result in a download of the allowed maximum amount of items. For anonymous users the allowed maximum amount is 50 search results.

    To select a subset of the search results, click "Selective Export" button and make a selection of the items you want to export. The amount of items that can be exported at once is similarly restricted as the full export.

    After making a selection, click one of the export format buttons. The amount of items that will be exported is indicated in the bubble next to export format.