The Hurst parameter and option pricing with fractional Brownian motion

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dc.contributor.advisor Van Zyl, A.J. en
dc.contributor.postgraduate Ostaszewicz, Anna Julia en
dc.date.accessioned 2013-09-07T06:25:57Z
dc.date.available 2013-04-25 en
dc.date.available 2013-09-07T06:25:57Z
dc.date.created 2013-04-17 en
dc.date.issued 2012 en
dc.date.submitted 2013-02-01 en
dc.description Dissertation (MSc)--University of Pretoria, 2012. en
dc.description.abstract 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. en
dc.description.availability unrestricted en
dc.description.department Mathematics and Applied Mathematics en
dc.identifier.citation Ostaszewicz, AJ 2012, The Hurst parameter and option pricing with fractional Brownian motion, MSc dissertation, University of Pretoria, Pretoria, viewed yymmdd < http://hdl.handle.net/2263/26521 > en
dc.identifier.other C13/4/94/gm en
dc.identifier.upetdurl http://upetd.up.ac.za/thesis/available/etd-02012013-134807/ en
dc.identifier.uri http://hdl.handle.net/2263/26521
dc.language.iso en
dc.publisher University of Pretoria en_ZA
dc.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 en
dc.subject Fractional brownian motion en
dc.subject Option pricing en
dc.subject Hurst parameter en
dc.subject UCTD en_US
dc.title The Hurst parameter and option pricing with fractional Brownian motion en
dc.type Dissertation en


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