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The Hurst parameter and option pricing with fractional Brownian motion
Dissertation (MSc)--University of Pretoria, 2012.
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| Format: | Thesis |
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University of Pretoria
2013
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| _version_ | 1867613514580885504 |
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| access_status_str | Open Access |
| author2 | Van Zyl, A.J. |
| author_browse | Van Zyl, A.J. |
| author_facet | Van Zyl, A.J. |
| collection | Thesis |
| dc_rights_str_mv | © 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 |
| description | Dissertation (MSc)--University of Pretoria, 2012. |
| format | Thesis |
| id | oai:repository.up.ac.za:2263/26521 |
| institution | University of Pretoria (South Africa) |
| last_indexed | 2026-06-10T12:37:21.635Z |
| license_str | Other — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from UPSpace — University of Pretoria Institutional Repository |
| publishDate | 2013 |
| publishDateRange | 2013 |
| publishDateSort | 2013 |
| publisher | University of Pretoria |
| publisherStr | University of Pretoria |
| record_format | dspace |
| source_str | UPSpace — University of Pretoria Institutional Repository |
| spelling | oai:repository.up.ac.za:2263/26521 The Hurst parameter and option pricing with fractional Brownian motion Van Zyl, A.J. ania.ostaszewicz@up.ac.za Ostaszewicz, Anna Julia Fractional brownian motion Option pricing Hurst parameter UCTD Dissertation (MSc)--University of Pretoria, 2012. 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. Mathematics and Applied Mathematics unrestricted 2013-09-07T06:25:57Z 2013-04-25 2013-09-07T06:25:57Z 2013-04-17 2012 2013-02-01 Dissertation 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 > C13/4/94/gm http://hdl.handle.net/2263/26521 http://upetd.up.ac.za/thesis/available/etd-02012013-134807/ © 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 application/pdf University of Pretoria |
| spellingShingle | Fractional brownian motion Option pricing Hurst parameter UCTD The Hurst parameter and option pricing with fractional Brownian motion |
| title | The Hurst parameter and option pricing with fractional Brownian motion |
| title_full | The Hurst parameter and option pricing with fractional Brownian motion |
| title_fullStr | The Hurst parameter and option pricing with fractional Brownian motion |
| title_full_unstemmed | The Hurst parameter and option pricing with fractional Brownian motion |
| title_short | The Hurst parameter and option pricing with fractional Brownian motion |
| title_sort | hurst parameter and option pricing with fractional brownian motion |
| topic | Fractional brownian motion Option pricing Hurst parameter UCTD |
| url | http://hdl.handle.net/2263/26521 http://upetd.up.ac.za/thesis/available/etd-02012013-134807/ |