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Model Misspecification and the Hedging of Exotic Options
Asset pricing models are well established and have been used extensively by practitioners both for pricing options as well as for hedging them. Though Black-Scholes is the original and most commonly communicated asset pricing model, alternative asset pricing models which incorporate additional featu...
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| Format: | Thesis |
| Language: | English |
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Department of Finance and Tax
2018
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| _version_ | 1867613206789226496 |
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| access_status_str | Open Access |
| author | Balshaw, Lloyd Stanley |
| author2 | Ouwehand, Peter |
| author_browse | Balshaw, Lloyd Stanley Ouwehand, Peter |
| author_facet | Ouwehand, Peter Balshaw, Lloyd Stanley |
| author_sort | Balshaw, Lloyd Stanley |
| collection | Thesis |
| description | Asset pricing models are well established and have been used extensively by practitioners both for pricing options as well as for hedging them. Though Black-Scholes is the original and most commonly communicated asset pricing model, alternative asset pricing models which incorporate additional features have since been developed. We present three asset pricing models here - the Black-Scholes model, the Heston model and the Merton (1976) model. For each asset pricing model we test the hedge effectiveness of delta hedging, minimum variance hedging and static hedging, where appropriate. The options hedged under the aforementioned techniques and asset pricing models are down-and-out call options, lookback options and cliquet options. The hedges are performed over three strikes, which represent At-the-money, Out-the-money and In-the-money options. Stock prices are simulated under the stochastic-volatility double jump diffusion (SVJJ) model, which incorporates stochastic volatility as well as jumps in the stock and volatility process. Simulation is performed under two ’Worlds’. World 1 is set under normal market conditions, whereas World 2 represents stressed market conditions. Calibrating each asset pricing model to observed option prices is performed via the use of a least squares optimisation routine. We find that there is not an asset pricing model which consistently provides a better hedge in World 1. In World 2, however, the Heston model marginally outperforms the Black-Scholes model overall. This can be explained through the higher volatility under World 2, which the Heston model can more accurately describe given the stochastic volatility component. Calibration difficulties are experienced with the Merton model. These difficulties lead to larger errors when minimum variance hedging and alternative calibration techniques should be considered for future users of the optimiser. |
| format | Thesis |
| id | oai:open.uct.ac.za:11427/28437 |
| institution | University of Cape Town (South Africa) |
| language | eng |
| last_indexed | 2026-06-10T12:32:27.580Z |
| license_str | Not specified — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from UCTD — University of Cape Town Open Access Repository |
| publishDate | 2018 |
| publishDateRange | 2018 |
| publishDateSort | 2018 |
| 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:11427/28437 Model Misspecification and the Hedging of Exotic Options Balshaw, Lloyd Stanley Ouwehand, Peter Model Misspecification Black-Scholes model pricing model Heston model Merton (1976) model Asset pricing models are well established and have been used extensively by practitioners both for pricing options as well as for hedging them. Though Black-Scholes is the original and most commonly communicated asset pricing model, alternative asset pricing models which incorporate additional features have since been developed. We present three asset pricing models here - the Black-Scholes model, the Heston model and the Merton (1976) model. For each asset pricing model we test the hedge effectiveness of delta hedging, minimum variance hedging and static hedging, where appropriate. The options hedged under the aforementioned techniques and asset pricing models are down-and-out call options, lookback options and cliquet options. The hedges are performed over three strikes, which represent At-the-money, Out-the-money and In-the-money options. Stock prices are simulated under the stochastic-volatility double jump diffusion (SVJJ) model, which incorporates stochastic volatility as well as jumps in the stock and volatility process. Simulation is performed under two ’Worlds’. World 1 is set under normal market conditions, whereas World 2 represents stressed market conditions. Calibrating each asset pricing model to observed option prices is performed via the use of a least squares optimisation routine. We find that there is not an asset pricing model which consistently provides a better hedge in World 1. In World 2, however, the Heston model marginally outperforms the Black-Scholes model overall. This can be explained through the higher volatility under World 2, which the Heston model can more accurately describe given the stochastic volatility component. Calibration difficulties are experienced with the Merton model. These difficulties lead to larger errors when minimum variance hedging and alternative calibration techniques should be considered for future users of the optimiser. 2018-09-09T12:38:53Z 2018-09-09T12:38:53Z 2018 2018-08-30T07:14:47Z Master Thesis Masters MPhil http://hdl.handle.net/11427/28437 eng application/pdf Department of Finance and Tax Faculty of Commerce University of Cape Town |
| spellingShingle | Model Misspecification Black-Scholes model pricing model Heston model Merton (1976) model Balshaw, Lloyd Stanley Model Misspecification and the Hedging of Exotic Options |
| thesis_degree_str | Master's |
| title | Model Misspecification and the Hedging of Exotic Options |
| title_full | Model Misspecification and the Hedging of Exotic Options |
| title_fullStr | Model Misspecification and the Hedging of Exotic Options |
| title_full_unstemmed | Model Misspecification and the Hedging of Exotic Options |
| title_short | Model Misspecification and the Hedging of Exotic Options |
| title_sort | model misspecification and the hedging of exotic options |
| topic | Model Misspecification Black-Scholes model pricing model Heston model Merton (1976) model |
| url | http://hdl.handle.net/11427/28437 |
| work_keys_str_mv | AT balshawlloydstanley modelmisspecificationandthehedgingofexoticoptions |