Markov-Switching models and resultant equity implied volatility surfaces: a South African application

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dc.contributor.advisorBecker, Ronalden_ZA
dc.contributor.authorFairbrother, Marken_ZA
dc.date.accessioned2014-12-28T20:11:43Z
dc.date.available2014-12-28T20:11:43Z
dc.date.issued2012en_ZA
dc.descriptionIncludes bibliographical references.en_ZA
dc.description.abstractStandard Geometric Brownian Motion is the stock model underlying Black-Scholes famous option pricing formula. There are however numerous problems with this stock model as certain features do not follow some empirical stylised facts we see from the observation of actual asset prices. In particular, the constant parameter idea behind Geometric Brownian Motion is flawed. It is argued that information flow dictates stock price movements and information is a function macro-economic regimes shifts. As such, we propose an alternative model, one in which the parameters in the Standard Geometric Brownian Motion change according to an underlying Hidden Markov Process. This new model, termed a Markov-Switching model, is presented in extensive detail. Parameter Estimation methods, Simulation Methods and Option Pricing Theory are explored. Summary algorithms are presented so that this dissertation may be used as a good reference guide for those wishing to apply Markov-Switching Models. The model is tested by fitting the model on South African data and using the discussed option theory to create various implied volatility surfaces. The surfaces produced appear to obey some of the empirical observations and theoretical ideas around expected implied volatility surfaces, indicating that the Markov-Switching model has some value for option pricing.en_ZA
dc.identifier.apacitationFairbrother, M. (2012). <i>Markov-Switching models and resultant equity implied volatility surfaces: a South African application</i>. (Thesis). University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics. Retrieved from http://hdl.handle.net/11427/10450en_ZA
dc.identifier.chicagocitationFairbrother, Mark. <i>"Markov-Switching models and resultant equity implied volatility surfaces: a South African application."</i> Thesis., University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics, 2012. http://hdl.handle.net/11427/10450en_ZA
dc.identifier.citationFairbrother, M. 2012. Markov-Switching models and resultant equity implied volatility surfaces: a South African application. University of Cape Town.en_ZA
dc.identifier.ris TY - Thesis / Dissertation AU - Fairbrother, Mark AB - Standard Geometric Brownian Motion is the stock model underlying Black-Scholes famous option pricing formula. There are however numerous problems with this stock model as certain features do not follow some empirical stylised facts we see from the observation of actual asset prices. In particular, the constant parameter idea behind Geometric Brownian Motion is flawed. It is argued that information flow dictates stock price movements and information is a function macro-economic regimes shifts. As such, we propose an alternative model, one in which the parameters in the Standard Geometric Brownian Motion change according to an underlying Hidden Markov Process. This new model, termed a Markov-Switching model, is presented in extensive detail. Parameter Estimation methods, Simulation Methods and Option Pricing Theory are explored. Summary algorithms are presented so that this dissertation may be used as a good reference guide for those wishing to apply Markov-Switching Models. The model is tested by fitting the model on South African data and using the discussed option theory to create various implied volatility surfaces. The surfaces produced appear to obey some of the empirical observations and theoretical ideas around expected implied volatility surfaces, indicating that the Markov-Switching model has some value for option pricing. DA - 2012 DB - OpenUCT DP - University of Cape Town LK - https://open.uct.ac.za PB - University of Cape Town PY - 2012 T1 - Markov-Switching models and resultant equity implied volatility surfaces: a South African application TI - Markov-Switching models and resultant equity implied volatility surfaces: a South African application UR - http://hdl.handle.net/11427/10450 ER - en_ZA
dc.identifier.urihttp://hdl.handle.net/11427/10450
dc.identifier.vancouvercitationFairbrother M. Markov-Switching models and resultant equity implied volatility surfaces: a South African application. [Thesis]. University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics, 2012 [cited yyyy month dd]. Available from: http://hdl.handle.net/11427/10450en_ZA
dc.language.isoengen_ZA
dc.publisher.departmentDepartment of Mathematics and Applied Mathematicsen_ZA
dc.publisher.facultyFaculty of Scienceen_ZA
dc.publisher.institutionUniversity of Cape Town
dc.subject.otherMathematics of Financeen_ZA
dc.titleMarkov-Switching models and resultant equity implied volatility surfaces: a South African applicationen_ZA
dc.typeMaster Thesis
dc.type.qualificationlevelMasters
dc.type.qualificationnameMScen_ZA
uct.type.filetypeText
uct.type.filetypeImage
uct.type.publicationResearchen_ZA
uct.type.resourceThesisen_ZA
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