The Lifted Heston Stochastic Volatility Model
dc.contributor.advisor | Backwell, Alex | |
dc.contributor.advisor | Soane, Andrew | |
dc.contributor.author | Broodryk, Ryan | |
dc.date.accessioned | 2021-01-21T07:29:56Z | |
dc.date.available | 2021-01-21T07:29:56Z | |
dc.date.issued | 2020 | |
dc.date.updated | 2021-01-04T12:14:02Z | |
dc.description.abstract | 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. | |
dc.identifier.apacitation | Broodryk, 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/11427/32614 | en_ZA |
dc.identifier.chicagocitation | Broodryk, 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/11427/32614 | en_ZA |
dc.identifier.citation | Broodryk, R. 2020. The Lifted Heston Stochastic Volatility Model. . ,Faculty of Commerce ,African Institute of Financial Markets and Risk Management. http://hdl.handle.net/11427/32614 | en_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.uri | http://hdl.handle.net/11427/32614 | |
dc.identifier.vancouvercitation | Broodryk 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/11427/32614 | en_ZA |
dc.language.rfc3066 | eng | |
dc.publisher.department | African Institute of Financial Markets and Risk Management | |
dc.publisher.faculty | Faculty of Commerce | |
dc.subject | Stochastic volatility | |
dc.subject | Implied volatility | |
dc.subject | Volatility Skew | |
dc.subject | Monte-Carlo | |
dc.subject | Cosine method | |
dc.subject | Riccati equations | |
dc.subject | Complexity analysis | |
dc.title | The Lifted Heston Stochastic Volatility Model | |
dc.type | Master Thesis | |
dc.type.qualificationlevel | Masters | |
dc.type.qualificationlevel | MPhil |