The Lifted Heston Stochastic Volatility Model

dc.contributor.advisorBackwell, Alex
dc.contributor.advisorSoane, Andrew
dc.contributor.authorBroodryk, Ryan
dc.date.accessioned2021-01-21T07:29:56Z
dc.date.available2021-01-21T07:29:56Z
dc.date.issued2020
dc.date.updated2021-01-04T12:14:02Z
dc.description.abstractCan we capture the explosive nature of volatility skew observed in the market, without resorting to non-Markovian models? We show that, in terms of skew, the Heston model cannot match the market at both long and short maturities simultaneously. We introduce Abi Jaber (2019)'s Lifted Heston model and explain how to price options with it using both the cosine method and standard Monte-Carlo techniques. This allows us to back out implied volatilities and compute skew for both models, confirming that the Lifted Heston nests the standard Heston model. We then produce and analyze the skew for Lifted Heston models with a varying number N of mean reverting terms, and give an empirical study into the time complexity of increasing N. We observe a weak increase in convergence speed in the cosine method for increased N, and comment on the number of factors to implement for practical use.
dc.identifier.apacitationBroodryk, R. (2020). <i>The Lifted Heston Stochastic Volatility Model</i>. (). ,Faculty of Commerce ,African Institute of Financial Markets and Risk Management. Retrieved from http://hdl.handle.net/11427/32614en_ZA
dc.identifier.chicagocitationBroodryk, Ryan. <i>"The Lifted Heston Stochastic Volatility Model."</i> ., ,Faculty of Commerce ,African Institute of Financial Markets and Risk Management, 2020. http://hdl.handle.net/11427/32614en_ZA
dc.identifier.citationBroodryk, R. 2020. The Lifted Heston Stochastic Volatility Model. . ,Faculty of Commerce ,African Institute of Financial Markets and Risk Management. http://hdl.handle.net/11427/32614en_ZA
dc.identifier.ris TY - Master Thesis AU - Broodryk, Ryan AB - Can we capture the explosive nature of volatility skew observed in the market, without resorting to non-Markovian models? We show that, in terms of skew, the Heston model cannot match the market at both long and short maturities simultaneously. We introduce Abi Jaber (2019)'s Lifted Heston model and explain how to price options with it using both the cosine method and standard Monte-Carlo techniques. This allows us to back out implied volatilities and compute skew for both models, confirming that the Lifted Heston nests the standard Heston model. We then produce and analyze the skew for Lifted Heston models with a varying number N of mean reverting terms, and give an empirical study into the time complexity of increasing N. We observe a weak increase in convergence speed in the cosine method for increased N, and comment on the number of factors to implement for practical use. DA - 2020_ DB - OpenUCT DP - University of Cape Town KW - Stochastic volatility KW - Implied volatility KW - Volatility Skew KW - Monte-Carlo KW - Cosine method KW - Riccati equations KW - Complexity analysis LK - https://open.uct.ac.za PY - 2020 T1 - The Lifted Heston Stochastic Volatility Model TI - The Lifted Heston Stochastic Volatility Model UR - http://hdl.handle.net/11427/32614 ER - en_ZA
dc.identifier.urihttp://hdl.handle.net/11427/32614
dc.identifier.vancouvercitationBroodryk R. The Lifted Heston Stochastic Volatility Model. []. ,Faculty of Commerce ,African Institute of Financial Markets and Risk Management, 2020 [cited yyyy month dd]. Available from: http://hdl.handle.net/11427/32614en_ZA
dc.language.rfc3066eng
dc.publisher.departmentAfrican Institute of Financial Markets and Risk Management
dc.publisher.facultyFaculty of Commerce
dc.subjectStochastic volatility
dc.subjectImplied volatility
dc.subjectVolatility Skew
dc.subjectMonte-Carlo
dc.subjectCosine method
dc.subjectRiccati equations
dc.subjectComplexity analysis
dc.titleThe Lifted Heston Stochastic Volatility Model
dc.typeMaster Thesis
dc.type.qualificationlevelMasters
dc.type.qualificationlevelMPhil
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