Van Zyl, A.J.2017-06-052017-06-052017-04-212015Richards, MT 2015, A finite element approach to pricing Barrier options, MSc Dissertation, University of Pretoria, Pretoria, viewed yymmdd <http://hdl.handle.net/2263/60854>A2017http://hdl.handle.net/2263/60854Dissertation (MSc)--University of Pretoria, 2015.In this dissertation we consider the valuation of discretely monitored barrier options under the in nite element method. The in nite element method is an extension to the standard nite element method that accepts problems with unbounded spacial domains (such as the Black-Scholes PDE), without resorting to domain truncation. The degeneracy of the Black-Scholes PDE when the underlying asset reaches zero, requires that the method be formulated within the context of weighted Sobolev spaces. We will demonstrate the convergence of the proposed method and provide a rigorous investigation into the underlying weighted Sobolev spaces in which the convergence is to be demonstrated.en© 2017 University of Pretoria. All rights reserved. The copyright in this work vests in the University of Pretoria. No part of this work may be reproduced or transmitted in any form or by any means, without the prior written permission of the University of Pretoria.UCTDDissertation28124082