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Asymptotics of the Rough Heston Model
The recent explosion of work on rough volatility and fractional Brownian motion has led to the development of a new generation of stochastic volatility models. Such models are able to capture a wide range of stylised facts that classical models simply do not. While these models have sound mathematic...
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| Format: | Thesis |
| Language: | English |
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Department of Finance and Tax
2022
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| _version_ | 1867613149435265024 |
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| access_status_str | Open Access |
| author | Hayes, Joshua J |
| author2 | Ouwehand, Peter |
| author_browse | Hayes, Joshua J Ouwehand, Peter |
| author_facet | Ouwehand, Peter Hayes, Joshua J |
| author_sort | Hayes, Joshua J |
| collection | Thesis |
| description | The recent explosion of work on rough volatility and fractional Brownian motion has led to the development of a new generation of stochastic volatility models. Such models are able to capture a wide range of stylised facts that classical models simply do not. While these models have sound mathematical underpinnings, they are difficult to implement, largely due to the fact that fractional Brownian motion is neither Markovian nor a semimartingale. One idea is to investigate the behaviour of these models as maturities become very small (or very large) and consider asymptotic estimates for quantities of interest. Here we investigate the performance of small-time asymptotic formulae for the cumulant generating function of the Fractional Heston model as presented in Guennoun et al. (2018). These formulae and their effectiveness for small-time pricing are interrogated and compared against the Rough Heston model proposed in El Euch and Rosenbaum (2019). |
| format | Thesis |
| id | oai:open.uct.ac.za:11427/35803 |
| institution | University of Cape Town (South Africa) |
| language | eng |
| last_indexed | 2026-06-10T12:31:31.816Z |
| license_str | Not specified — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from UCTD — University of Cape Town Open Access Repository |
| publishDate | 2022 |
| publishDateRange | 2022 |
| publishDateSort | 2022 |
| publisher | Department of Finance and Tax |
| publisherStr | Department of Finance and Tax |
| record_format | dspace |
| source_str | UCTD — University of Cape Town Open Access Repository |
| spelling | oai:open.uct.ac.za:11427/35803 Asymptotics of the Rough Heston Model Hayes, Joshua J Ouwehand, Peter Mathematical Finance The recent explosion of work on rough volatility and fractional Brownian motion has led to the development of a new generation of stochastic volatility models. Such models are able to capture a wide range of stylised facts that classical models simply do not. While these models have sound mathematical underpinnings, they are difficult to implement, largely due to the fact that fractional Brownian motion is neither Markovian nor a semimartingale. One idea is to investigate the behaviour of these models as maturities become very small (or very large) and consider asymptotic estimates for quantities of interest. Here we investigate the performance of small-time asymptotic formulae for the cumulant generating function of the Fractional Heston model as presented in Guennoun et al. (2018). These formulae and their effectiveness for small-time pricing are interrogated and compared against the Rough Heston model proposed in El Euch and Rosenbaum (2019). 2022-02-22T04:08:57Z 2022-02-22T04:08:57Z 2021 2022-02-16T06:05:26Z Master Thesis Masters MPhil http://hdl.handle.net/11427/35803 eng application/pdf Department of Finance and Tax Faculty of Commerce |
| spellingShingle | Mathematical Finance Hayes, Joshua J Asymptotics of the Rough Heston Model |
| thesis_degree_str | Master's |
| title | Asymptotics of the Rough Heston Model |
| title_full | Asymptotics of the Rough Heston Model |
| title_fullStr | Asymptotics of the Rough Heston Model |
| title_full_unstemmed | Asymptotics of the Rough Heston Model |
| title_short | Asymptotics of the Rough Heston Model |
| title_sort | asymptotics of the rough heston model |
| topic | Mathematical Finance |
| url | http://hdl.handle.net/11427/35803 |
| work_keys_str_mv | AT hayesjoshuaj asymptoticsoftheroughhestonmodel |