Library Portal | UWC Portal | National ETDs | Global ETDs
    • Login
    Contact Us | About Us | FAQs | Login
    View Item 
    •   ETD Home
    • Faculty of Natural Science
    • Department of Mathematics
    • Philosophiae Doctor - PhD (Mathematics)
    • View Item
    •   ETD Home
    • Faculty of Natural Science
    • Department of Mathematics
    • Philosophiae Doctor - PhD (Mathematics)
    • View Item
    JavaScript is disabled for your browser. Some features of this site may not work without it.

    Numerical singular perturbation approaches based on spline approximation methods for solving problems in computational finance

    Thumbnail
    View/Open
    Khabir_phd_Math_2011.pdf (86.57Mb)
    Date
    2011
    Author
    Kabir, Mohmed Hassan Mohmed
    Metadata
    Show full item record
    Abstract
    Options are a special type of derivative securities because their values are derived from the value of some underlying security. Most options can be grouped into either of the two categories: European options which can be exercised only on the expiration date, and American options which can be exercised on or before the expiration date. American options are much harder to deal with than European ones. The reason being the optimal exercise policy of these options which led to free boundary problems. Ever since the seminal work of Black and Scholes [J. Pol. Bean. 81(3) (1973), 637-659], the differential equation approach in pricing options has attracted many researchers. Recently, numerical singular perturbation techniques have been used extensively for solving many differential equation models of sciences and engineering. In this thesis, we explore some of those methods which are based on spline approximations to solve the option pricing problems. We show a systematic construction and analysis of these methods to solve some European option problems and then extend the approach to solve problems of pricing American options as well as some exotic options. Proposed methods are analyzed for stability and convergence. Thorough numerical results are presented and compared with those seen in the literature.
    URI
    http://hdl.handle.net/11394/8810
    Collections
    • Philosophiae Doctor - PhD (Mathematics)

    DSpace 6.3 | Ubuntu | Copyright © University of the Western Cape
    Contact Us | Send Feedback
    Theme by 
    @mire NV
     

     

    Browse

    All of RepositoryCommunities & CollectionsBy Issue DateAuthorsTitlesSubjectsThis CollectionBy Issue DateAuthorsTitlesSubjects

    My Account

    Login

    Statistics

    View Usage Statistics

    DSpace 6.3 | Ubuntu | Copyright © University of the Western Cape
    Contact Us | Send Feedback
    Theme by 
    @mire NV