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Parsimonious Mixed Bergomi Models for VIX Derivatives: Calibration and Estimation via Quantization
Thesis (PhD)--Stellenbosch University, 2026.
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| Format: | Thesis |
| Language: | English |
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Stellenbosch : Stellenbosch University
2026
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| _version_ | 1867613949793402880 |
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| access_status_str | Open Access |
| author | Kyakutwika, Nelson |
| author2 | Alfeus, Mesias |
| author_browse | Alfeus, Mesias Kyakutwika, Nelson |
| author_facet | Alfeus, Mesias Kyakutwika, Nelson |
| author_sort | Kyakutwika, Nelson |
| collection | Thesis |
| dc_rights_str_mv | Stellenbosch University |
| description | Thesis (PhD)--Stellenbosch University, 2026. |
| format | Thesis |
| id | oai:scholar.sun.ac.za:10019.1/136205 |
| institution | Stellenbosch University (South Africa) |
| language | English |
| last_indexed | 2026-06-10T12:44:16.501Z |
| license_str | Other — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from SUNScholar — Stellenbosch University Repository |
| publishDate | 2026 |
| publishDateRange | 2026 |
| publishDateSort | 2026 |
| publisher | Stellenbosch : Stellenbosch University |
| publisherStr | Stellenbosch : Stellenbosch University |
| record_format | dspace |
| source_str | SUNScholar — Stellenbosch University Repository |
| spelling | oai:scholar.sun.ac.za:10019.1/136205 Parsimonious Mixed Bergomi Models for VIX Derivatives: Calibration and Estimation via Quantization Kyakutwika, Nelson Alfeus, Mesias Schlogl, Erik Bartlett, Bruce Stellenbosch University. Faculty of Science. Dept. of Mathematical Sciences. Thesis (PhD)--Stellenbosch University, 2026. Kyakutwika, N. 2026. Parsimonious Mixed Bergomi Models for VIX Derivatives: Calibration and Estimation via Quantization. Unpublished doctoral dissertation. Stellenbosch: Stellenbosch University [online]. Available: https://scholar.sun.ac.za/items/89ad45d0-38ae-401e-bc1c-8ac0d73a7795 VIX futures and options are among the world’s most liquid derivatives. Mixed Bergomi models are known to fit VIX futures and options well; however, they are not fast enough for calibration over extended time scales. In addition, the models are over-parameterised and lack dynamic estimation frameworks that incorporate both time-series and cross-sectional features of the VIX market. This dissertation addresses these challenges by developing a fast and parsimonious framework for calibrating and estimating mixed Bergomi models for VIX derivatives. We adapt vector quantization for use in mixed Bergomi models to replace the computationally slow quadrature techniques. Using this fast pricing approach, we empirically derive parsimonious variants of mixed Bergomi models. We then estimate these parsimonious models using the Unscented Kalman Filter (UKF). This dissertation makes four key contributions. First, we develop a fast pricing technique that reduces computational time in mixed Bergomi models by up to a factor of 120. Second, we introduce parsimonious variants of the classical models that fit the daily VIX option surface with approximately a quarter of the number of parameters used by the classical models, with a marginal loss in accuracy. Third, model estimation using the UKF enables joint time-series and cross-sectional analysis of the VIX market – a novel application in this class of models. Finally, we validate our model frameworks using extensive simulations before applying them to market data. Doctoral 2026-04-28T08:45:11Z 2026-04-28T08:45:11Z 2026-03 Thesis https://scholar.sun.ac.za/handle/10019.1/136205 en Stellenbosch University 120 pages application/pdf Stellenbosch : Stellenbosch University |
| spellingShingle | Kyakutwika, Nelson Parsimonious Mixed Bergomi Models for VIX Derivatives: Calibration and Estimation via Quantization |
| title | Parsimonious Mixed Bergomi Models for VIX Derivatives: Calibration and Estimation via Quantization |
| title_full | Parsimonious Mixed Bergomi Models for VIX Derivatives: Calibration and Estimation via Quantization |
| title_fullStr | Parsimonious Mixed Bergomi Models for VIX Derivatives: Calibration and Estimation via Quantization |
| title_full_unstemmed | Parsimonious Mixed Bergomi Models for VIX Derivatives: Calibration and Estimation via Quantization |
| title_short | Parsimonious Mixed Bergomi Models for VIX Derivatives: Calibration and Estimation via Quantization |
| title_sort | parsimonious mixed bergomi models for vix derivatives calibration and estimation via quantization |
| url | https://scholar.sun.ac.za/handle/10019.1/136205 |
| work_keys_str_mv | AT kyakutwikanelson parsimoniousmixedbergomimodelsforvixderivativescalibrationandestimationviaquantization |