Portfolio risk measures and option pricing under a Hybrid Brownian motion model

dc.contributor.advisorVan Zyl, Gusti
dc.contributor.coadvisorKufakunesu, Rodwell
dc.contributor.emailinmbona@gmail.comen_ZA
dc.contributor.postgraduateMbona, Innocent
dc.date.accessioned2018-02-23T07:55:25Z
dc.date.available2018-02-23T07:55:25Z
dc.date.created2018-04-23
dc.date.issued2017
dc.descriptionDissertation (MSc)--University of Pretoria, 2017.en_ZA
dc.description.abstractThe 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.en_ZA
dc.description.availabilityUnrestricteden_ZA
dc.description.degreeMScen_ZA
dc.description.departmentMathematics and Applied Mathematicsen_ZA
dc.description.sponsorshipNational Research Fund (NRF), University of Pretoria Postgraduate bursary and the General Studentship bursaryen_ZA
dc.identifier.citationMbona, 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>en_ZA
dc.identifier.otherA2018en_ZA
dc.identifier.urihttp://hdl.handle.net/2263/64068
dc.language.isoenen_ZA
dc.publisherUniversity of Pretoria
dc.rights© 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.
dc.subjectHybrid modelen_ZA
dc.subjectOption pricingen_ZA
dc.subjectHedgingen_ZA
dc.subjectVaR and Expected Shortfallen_ZA
dc.subjectFat-tailed distributionen_ZA
dc.subjectUCTD
dc.titlePortfolio risk measures and option pricing under a Hybrid Brownian motion modelen_ZA
dc.typeDissertationen_ZA

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