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Pricing American/Bermudan-style Options under Stochastic Volatility
A method to price American options under a stochastic volatility framework is introduced which is based on Rambharat and Brockwell (2010). We price American options under the Heston and Bates stochastic volatility models where volatility is assumed to be a latent process. The pricing algorithm is ba...
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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_ | 1867613507949690880 |
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| access_status_str | Open Access |
| author | Jankelow, Adam |
| author2 | Ouwehand, Peter |
| author_browse | Jankelow, Adam Ouwehand, Peter |
| author_facet | Ouwehand, Peter Jankelow, Adam |
| author_sort | Jankelow, Adam |
| collection | Thesis |
| description | A method to price American options under a stochastic volatility framework is introduced which is based on Rambharat and Brockwell (2010). We price American options under the Heston and Bates stochastic volatility models where volatility is assumed to be a latent process. The pricing algorithm is based on the least-squares Monte Carlo approach made popular by Longstaff and Schwartz (2001). Information about the volatility of the underlying asset is used to assist in solving the pricing problem. Since volatility is assumed to be a latent, a particle filter is used to estimate the filtering distribution of volatility. A summary vector is constructed which captures the essential features of the filtering distribution. At each time step before maturity, the elements of the summary vector and the current share price are used as explanatory variables in a regression function which estimates the continuation value of the option. Estimating the continuation value assists in finding the optimal time to exercise the option. This pricing approach is benchmarked against a method which assumes volatility is observable. Furthermore, our pricing approach is compared to simpler methods which do not use particle filtering. Results from our numerical experiments suggest the proposed approach produces accurate option prices. |
| format | Thesis |
| id | oai:open.uct.ac.za:11427/32755 |
| institution | University of Cape Town (South Africa) |
| language | eng |
| last_indexed | 2026-06-10T12:37:15.504Z |
| 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:11427/32755 Pricing American/Bermudan-style Options under Stochastic Volatility Jankelow, Adam Ouwehand, Peter Mathematical Finance A method to price American options under a stochastic volatility framework is introduced which is based on Rambharat and Brockwell (2010). We price American options under the Heston and Bates stochastic volatility models where volatility is assumed to be a latent process. The pricing algorithm is based on the least-squares Monte Carlo approach made popular by Longstaff and Schwartz (2001). Information about the volatility of the underlying asset is used to assist in solving the pricing problem. Since volatility is assumed to be a latent, a particle filter is used to estimate the filtering distribution of volatility. A summary vector is constructed which captures the essential features of the filtering distribution. At each time step before maturity, the elements of the summary vector and the current share price are used as explanatory variables in a regression function which estimates the continuation value of the option. Estimating the continuation value assists in finding the optimal time to exercise the option. This pricing approach is benchmarked against a method which assumes volatility is observable. Furthermore, our pricing approach is compared to simpler methods which do not use particle filtering. Results from our numerical experiments suggest the proposed approach produces accurate option prices. 2021-02-02T19:50:24Z 2021-02-02T19:50:24Z 2020 2021-01-29T08:23:32Z Master Thesis Masters MPhil http://hdl.handle.net/11427/32755 eng application/pdf African Institute of Financial Markets and Risk Management Faculty of Commerce |
| spellingShingle | Mathematical Finance Jankelow, Adam Pricing American/Bermudan-style Options under Stochastic Volatility |
| thesis_degree_str | Master's |
| title | Pricing American/Bermudan-style Options under Stochastic Volatility |
| title_full | Pricing American/Bermudan-style Options under Stochastic Volatility |
| title_fullStr | Pricing American/Bermudan-style Options under Stochastic Volatility |
| title_full_unstemmed | Pricing American/Bermudan-style Options under Stochastic Volatility |
| title_short | Pricing American/Bermudan-style Options under Stochastic Volatility |
| title_sort | pricing american bermudan style options under stochastic volatility |
| topic | Mathematical Finance |
| url | http://hdl.handle.net/11427/32755 |
| work_keys_str_mv | AT jankelowadam pricingamericanbermudanstyleoptionsunderstochasticvolatility |