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Portfolio risk measures and option pricing under a Hybrid Brownian motion model
Dissertation (MSc)--University of Pretoria, 2017.
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| Format: | Thesis |
| Language: | English |
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University of Pretoria
2018
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| _version_ | 1867613535738003456 |
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| access_status_str | Open Access |
| author2 | Van Zyl, Gusti |
| author_browse | Van Zyl, Gusti |
| author_facet | Van Zyl, Gusti |
| collection | Thesis |
| dc_rights_str_mv | © 2018 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, 2017. |
| format | Thesis |
| id | oai:repository.up.ac.za:2263/64068 |
| institution | University of Pretoria (South Africa) |
| language | English |
| last_indexed | 2026-06-10T12:37:41.969Z |
| license_str | Other — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from UPSpace — University of Pretoria Institutional Repository |
| publishDate | 2018 |
| publishDateRange | 2018 |
| publishDateSort | 2018 |
| 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:2263/64068 Portfolio risk measures and option pricing under a Hybrid Brownian motion model Van Zyl, Gusti inmbona@gmail.com Kufakunesu, Rodwell Mbona, Innocent Hybrid model Option pricing Hedging VaR and Expected Shortfall Fat-tailed distribution UCTD Dissertation (MSc)--University of Pretoria, 2017. The 2008/9 financial crisis intensified the search for realistic return models, that capture real market movements. The assumed underlying statistical distribution of financial returns plays a crucial role in the evaluation of risk measures, and pricing of financial instruments. In this dissertation, we discuss an empirical study on the evaluation of the traditional portfolio risk measures, and option pricing under the hybrid Brownian motion model, developed by Shaw and Schofield. Under this model, we derive probability density functions that have a fat-tailed property, such that “25-sigma” or worse events are more probable. We then estimate Value-at-Risk (VaR) and Expected Shortfall (ES) using four equity stocks listed on the Johannesburg Stock Exchange, including the FTSE/JSE Top 40 index. We apply the historical method and Variance-Covariance method (VC) in the valuation of VaR. Under the VC method, we adopt the GARCH(1,1) model to deal with the volatility clustering phenomenon. We backtest the VaR results and discuss our findings for each probability density function. Furthermore, we apply the hybrid model to price European style options. We compare the pricing performance of the hybrid model to the classical Black-Scholes model. National Research Fund (NRF), University of Pretoria Postgraduate bursary and the General Studentship bursary Mathematics and Applied Mathematics MSc Unrestricted 2018-02-23T07:55:25Z 2018-02-23T07:55:25Z 2018-04-23 2017 Dissertation Mbona, IN 2017, Portfolio risk measures and option pricing under a Hybrid Brownian motion model, MSc Dissertation, University of Pretoria, Pretoria, viewed yymmdd <http://hdl.handle.net/2263/64068> A2018 http://hdl.handle.net/2263/64068 en © 2018 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 | Hybrid model Option pricing Hedging VaR and Expected Shortfall Fat-tailed distribution UCTD Portfolio risk measures and option pricing under a Hybrid Brownian motion model |
| title | Portfolio risk measures and option pricing under a Hybrid Brownian motion model |
| title_full | Portfolio risk measures and option pricing under a Hybrid Brownian motion model |
| title_fullStr | Portfolio risk measures and option pricing under a Hybrid Brownian motion model |
| title_full_unstemmed | Portfolio risk measures and option pricing under a Hybrid Brownian motion model |
| title_short | Portfolio risk measures and option pricing under a Hybrid Brownian motion model |
| title_sort | portfolio risk measures and option pricing under a hybrid brownian motion model |
| topic | Hybrid model Option pricing Hedging VaR and Expected Shortfall Fat-tailed distribution UCTD |
| url | http://hdl.handle.net/2263/64068 |