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The Lifted Heston Stochastic Volatility Model
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...
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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_ | 1867613249701150720 |
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| access_status_str | Open Access |
| author | Broodryk, Ryan |
| author2 | Backwell, Alex |
| author_browse | Backwell, Alex Broodryk, Ryan |
| author_facet | Backwell, Alex Broodryk, Ryan |
| author_sort | Broodryk, Ryan |
| collection | Thesis |
| description | 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. |
| format | Thesis |
| id | oai:open.uct.ac.za:11427/32614 |
| institution | University of Cape Town (South Africa) |
| language | eng |
| last_indexed | 2026-06-10T12:33:08.525Z |
| 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:11427/32614 The Lifted Heston Stochastic Volatility Model Broodryk, Ryan Backwell, Alex Soane, Andrew Stochastic volatility Implied volatility Volatility Skew Monte-Carlo Cosine method Riccati equations Complexity analysis 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. 2021-01-21T07:29:56Z 2021-01-21T07:29:56Z 2020 2021-01-04T12:14:02Z Master Thesis Masters MPhil http://hdl.handle.net/11427/32614 eng application/pdf African Institute of Financial Markets and Risk Management Faculty of Commerce |
| spellingShingle | Stochastic volatility Implied volatility Volatility Skew Monte-Carlo Cosine method Riccati equations Complexity analysis Broodryk, Ryan The Lifted Heston Stochastic Volatility Model |
| thesis_degree_str | Master's |
| title | The Lifted Heston Stochastic Volatility Model |
| title_full | The Lifted Heston Stochastic Volatility Model |
| title_fullStr | The Lifted Heston Stochastic Volatility Model |
| title_full_unstemmed | The Lifted Heston Stochastic Volatility Model |
| title_short | The Lifted Heston Stochastic Volatility Model |
| title_sort | lifted heston stochastic volatility model |
| topic | Stochastic volatility Implied volatility Volatility Skew Monte-Carlo Cosine method Riccati equations Complexity analysis |
| url | http://hdl.handle.net/11427/32614 |
| work_keys_str_mv | AT broodrykryan theliftedhestonstochasticvolatilitymodel AT broodrykryan liftedhestonstochasticvolatilitymodel |