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Highly efficient pricing of exotic derivatives under mean-reversion, jumps and stochastic volatility
The pricing of exotic derivatives continues to attract much attention from academics and practitioners alike. Despite the overwhelming interest, the task of finding a robust methodology that could derive closed-form solutions for exotic derivatives remains a difficult challenge. In addition, the lev...
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| Format: | Thesis |
| Language: | English |
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School of Management Studies
2019
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| _version_ | 1867613257609510912 |
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| access_status_str | Open Access |
| author | Huang, Chun-Sung |
| author2 | Mataramvura, Sure |
| author_browse | Huang, Chun-Sung Mataramvura, Sure |
| author_facet | Mataramvura, Sure Huang, Chun-Sung |
| author_sort | Huang, Chun-Sung |
| collection | Thesis |
| description | The pricing of exotic derivatives continues to attract much attention from academics and practitioners alike. Despite the overwhelming interest, the task of finding a robust methodology that could derive closed-form solutions for exotic derivatives remains a difficult challenge. In addition, the level of sophistication is greatly enhanced when options are priced in a more realistic framework. This includes, but not limited to, utilising jump-diffusion models with mean-reversion, stochastic volatility, and/or stochastic jump intensity. More pertinently, these inclusions allow the resulting asset price process to capture the various empirical features, such as heavy tails and asymmetry, commonly observed in financial data. However, under such a framework, the density function governing the underlying asset price process is generally not available. This leads to a breakdown of the classical risk-neutral option valuation method via the discounted expectation of the final payoff. Furthermore, when an analytical expression for the option pricing formula becomes available, the solution is often complex and in semi closed-form. Hence, a substantial amount of computational time is required to obtain the value of the option, which may not satisfy the efficiency demanded in practice. Such drawbacks may be remedied by utilising numerical integration techniques to price options more efficiently in the Fourier domain instead, since the associated characteristic functions are more readily available. This thesis is concerned primarily with the efficient and accurate pricing of exotic derivatives under the aforementioned framework. We address the research opportunity by exploring the valuation of exotic options with numerical integration techniques once the associated characteristic functions are developed. In particular, we advocate the use of the novel Fourier-cosine (COS) expansions, and the more recent Shannon wavelet inverse Fourier technique (SWIFT). Once the option prices are obtained, the efficiency of the two techniques are benchmarked against the widely-acclaimed fast Fourier transform (FFT) method. More importantly, we perform extensive numerical experiments and error analyses to show that, under our proposed framework, not only is the COS and SWIFT methods more efficient, but are also highly accurate with exponential rate of error convergence. Finally, we conduct a set of sensitivity analyses to evaluate the models’ consistency and robustness under different market conditions |
| format | Thesis |
| id | oai:open.uct.ac.za:11427/29243 |
| institution | University of Cape Town (South Africa) |
| language | eng |
| last_indexed | 2026-06-10T12:33:15.376Z |
| license_str | Not specified — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from UCTD — University of Cape Town Open Access Repository |
| publishDate | 2019 |
| publishDateRange | 2019 |
| publishDateSort | 2019 |
| publisher | School of Management Studies |
| publisherStr | School of Management Studies |
| record_format | dspace |
| source_str | UCTD — University of Cape Town Open Access Repository |
| spelling | oai:open.uct.ac.za:11427/29243 Highly efficient pricing of exotic derivatives under mean-reversion, jumps and stochastic volatility Huang, Chun-Sung Mataramvura, Sure O'Hara, John Computational Finance The pricing of exotic derivatives continues to attract much attention from academics and practitioners alike. Despite the overwhelming interest, the task of finding a robust methodology that could derive closed-form solutions for exotic derivatives remains a difficult challenge. In addition, the level of sophistication is greatly enhanced when options are priced in a more realistic framework. This includes, but not limited to, utilising jump-diffusion models with mean-reversion, stochastic volatility, and/or stochastic jump intensity. More pertinently, these inclusions allow the resulting asset price process to capture the various empirical features, such as heavy tails and asymmetry, commonly observed in financial data. However, under such a framework, the density function governing the underlying asset price process is generally not available. This leads to a breakdown of the classical risk-neutral option valuation method via the discounted expectation of the final payoff. Furthermore, when an analytical expression for the option pricing formula becomes available, the solution is often complex and in semi closed-form. Hence, a substantial amount of computational time is required to obtain the value of the option, which may not satisfy the efficiency demanded in practice. Such drawbacks may be remedied by utilising numerical integration techniques to price options more efficiently in the Fourier domain instead, since the associated characteristic functions are more readily available. This thesis is concerned primarily with the efficient and accurate pricing of exotic derivatives under the aforementioned framework. We address the research opportunity by exploring the valuation of exotic options with numerical integration techniques once the associated characteristic functions are developed. In particular, we advocate the use of the novel Fourier-cosine (COS) expansions, and the more recent Shannon wavelet inverse Fourier technique (SWIFT). Once the option prices are obtained, the efficiency of the two techniques are benchmarked against the widely-acclaimed fast Fourier transform (FFT) method. More importantly, we perform extensive numerical experiments and error analyses to show that, under our proposed framework, not only is the COS and SWIFT methods more efficient, but are also highly accurate with exponential rate of error convergence. Finally, we conduct a set of sensitivity analyses to evaluate the models’ consistency and robustness under different market conditions 2019-02-04T11:51:45Z 2019-02-04T11:51:45Z 2018 2019-02-02T09:28:31Z Doctoral Thesis Doctoral PhD http://hdl.handle.net/11427/29243 eng application/pdf School of Management Studies Faculty of Commerce University of Cape Town |
| spellingShingle | Computational Finance Huang, Chun-Sung Highly efficient pricing of exotic derivatives under mean-reversion, jumps and stochastic volatility |
| thesis_degree_str | Doctoral |
| title | Highly efficient pricing of exotic derivatives under mean-reversion, jumps and stochastic volatility |
| title_full | Highly efficient pricing of exotic derivatives under mean-reversion, jumps and stochastic volatility |
| title_fullStr | Highly efficient pricing of exotic derivatives under mean-reversion, jumps and stochastic volatility |
| title_full_unstemmed | Highly efficient pricing of exotic derivatives under mean-reversion, jumps and stochastic volatility |
| title_short | Highly efficient pricing of exotic derivatives under mean-reversion, jumps and stochastic volatility |
| title_sort | highly efficient pricing of exotic derivatives under mean reversion jumps and stochastic volatility |
| topic | Computational Finance |
| url | http://hdl.handle.net/11427/29243 |
| work_keys_str_mv | AT huangchunsung highlyefficientpricingofexoticderivativesundermeanreversionjumpsandstochasticvolatility |