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.

    Robust Spectral Methods for Solving Option Pricing Problems

    Thumbnail
    View/Open
    Thesis (3.190Mb)
    Date
    2012
    Author
    Pindza, Edson
    Metadata
    Show full item record
    Abstract
    Robust Spectral Methods for Solving Option Pricing Problems by Edson Pindza PhD thesis, Department of Mathematics and Applied Mathematics, Faculty of Natural Sciences, University of the Western Cape Ever since the invention of the classical Black-Scholes formula to price the financial derivatives, a number of mathematical models have been proposed by numerous researchers in this direction. Many of these models are in general very complex, thus closed form analytical solutions are rarely obtainable. In view of this, we present a class of efficient spectral methods to numerically solve several mathematical models of pricing options. We begin with solving European options. Then we move to solve their American counterparts which involve a free boundary and therefore normally difficult to price by other conventional numerical methods. We obtain very promising results for the above two types of options and therefore we extend this approach to solve some more difficult problems for pricing options, viz., jump-diffusion models and local volatility models. The numerical methods involve solving partial differential equations, partial integro-differential equations and associated complementary problems which are used to model the financial derivatives. In order to retain their exponential accuracy, we discuss the necessary modification of the spectral methods. Finally, we present several comparative numerical results showing the superiority of our spectral methods.
    URI
    http://hdl.handle.net/11394/4092
    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