In the mathematical modeling of the classical option pricing models it is assumed that the underlying stock price process follows a geometric Brownian motion, but through statistical analysis persistency was found in the log-returns of some South African stocks and Brownian motion does not have persistency. We suggest the replacement of Brownian motion with fractional Brownian motion which is a Gaussian process that depends on the Hurst parameter that allows for the modeling of autocorrelation in price returns. Three fractional Black-Scholes (Black) models were investigated where the underlying is assumed to follow a fractional Brownian motion. Using South African options on futures and warrant prices these models were compared to the classical models. / Dissertation (MSc)--University of Pretoria, 2012. / Mathematics and Applied Mathematics / unrestricted
| Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:up/oai:repository.up.ac.za:2263/26521 |
| Date | 01 February 2013 |
| Creators | Ostaszewicz, Anna Julia |
| Contributors | Van Zyl, A.J., ania.ostaszewicz@up.ac.za |
| Publisher | University of Pretoria |
| Source Sets | South African National ETD Portal |
| Detected Language | English |
| Type | Dissertation |
| Rights | © 2012 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 |
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