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Local Stochastic Volatility—The Hyp-Hyp Model
Volatility modelling is used predominantly in order to explain the volatility smile observed in the market. Stochastic volatility models are mainly used to capture the curvature of a volatility smile while local volatility models generally model the skew. Jackel and Kahl ¨ (2008) present a hyperboli...
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| Format: | Thesis |
| Language: | English |
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African Institute of Financial Markets and Risk Management
2021
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| _version_ | 1867613254566543360 |
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| access_status_str | Open Access |
| author | Cowen, Nicholas |
| author2 | McWalter, Thomas |
| author_browse | Cowen, Nicholas McWalter, Thomas |
| author_facet | McWalter, Thomas Cowen, Nicholas |
| author_sort | Cowen, Nicholas |
| collection | Thesis |
| description | Volatility modelling is used predominantly in order to explain the volatility smile observed in the market. Stochastic volatility models are mainly used to capture the curvature of a volatility smile while local volatility models generally model the skew. Jackel and Kahl ¨ (2008) present a hyperbolic-local hyperbolic-stochastic volatility (Hyp-Hyp) model which aims to improve upon existing local and stochastic volatility models such as the stochastic alpha, beta, rho (SABR) and constant elasticity of variance (CEV) models. The advantageous features of the Hyp-Hyp model are corroborated by implementing the model. Jackel and Kahl ¨ (2008) investigate the accuracy of a scaled analytical approximation for implied volatility, based on approximations presented by Watanabe (1987) and Fouque et al. (2000), for the Hyp-Hyp model. They use the approximation to derive an expression for the delta of an option. This dissertation analyses the Hyp-Hyp model, as well as the approximation, by deriving expressions for other sensitivities and by investigating the effect of the Hyp-Hyp model parameters on the volatility smile. The accuracy of the analytical approximation for functional forms other than those defined by the Hyp-Hyp model is explored. A derivation of the approximation is undertaken, presenting corrections to the expressions introduced by Kahl (2007) and used by Jackel and Kahl ¨ (2008). |
| format | Thesis |
| id | oai:open.uct.ac.za:11427/32556 |
| institution | University of Cape Town (South Africa) |
| language | eng |
| last_indexed | 2026-06-10T12:33:13.838Z |
| license_str | Not specified — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from UCTD — University of Cape Town Open Access Repository |
| publishDate | 2021 |
| publishDateRange | 2021 |
| publishDateSort | 2021 |
| publisher | African Institute of Financial Markets and Risk Management |
| publisherStr | African Institute of Financial Markets and Risk Management |
| record_format | dspace |
| source_str | UCTD — University of Cape Town Open Access Repository |
| spelling | oai:open.uct.ac.za:11427/32556 Local Stochastic Volatility—The Hyp-Hyp Model Cowen, Nicholas McWalter, Thomas Kienitz, Jorg Mathematical Finance Volatility modelling is used predominantly in order to explain the volatility smile observed in the market. Stochastic volatility models are mainly used to capture the curvature of a volatility smile while local volatility models generally model the skew. Jackel and Kahl ¨ (2008) present a hyperbolic-local hyperbolic-stochastic volatility (Hyp-Hyp) model which aims to improve upon existing local and stochastic volatility models such as the stochastic alpha, beta, rho (SABR) and constant elasticity of variance (CEV) models. The advantageous features of the Hyp-Hyp model are corroborated by implementing the model. Jackel and Kahl ¨ (2008) investigate the accuracy of a scaled analytical approximation for implied volatility, based on approximations presented by Watanabe (1987) and Fouque et al. (2000), for the Hyp-Hyp model. They use the approximation to derive an expression for the delta of an option. This dissertation analyses the Hyp-Hyp model, as well as the approximation, by deriving expressions for other sensitivities and by investigating the effect of the Hyp-Hyp model parameters on the volatility smile. The accuracy of the analytical approximation for functional forms other than those defined by the Hyp-Hyp model is explored. A derivation of the approximation is undertaken, presenting corrections to the expressions introduced by Kahl (2007) and used by Jackel and Kahl ¨ (2008). 2021-01-19T12:01:24Z 2021-01-19T12:01:24Z 2020 2021-01-19T11:08:07Z Master Thesis Masters MPhil http://hdl.handle.net/11427/32556 eng application/pdf African Institute of Financial Markets and Risk Management Faculty of Commerce |
| spellingShingle | Mathematical Finance Cowen, Nicholas Local Stochastic Volatility—The Hyp-Hyp Model |
| thesis_degree_str | Master's |
| title | Local Stochastic Volatility—The Hyp-Hyp Model |
| title_full | Local Stochastic Volatility—The Hyp-Hyp Model |
| title_fullStr | Local Stochastic Volatility—The Hyp-Hyp Model |
| title_full_unstemmed | Local Stochastic Volatility—The Hyp-Hyp Model |
| title_short | Local Stochastic Volatility—The Hyp-Hyp Model |
| title_sort | local stochastic volatility the hyp hyp model |
| topic | Mathematical Finance |
| url | http://hdl.handle.net/11427/32556 |
| work_keys_str_mv | AT cowennicholas localstochasticvolatilitythehyphypmodel |