Parsimonious Mixed Bergomi Models for VIX Derivatives: Calibration and Estimation via Quantization

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.

Grantor dc:publisher

Stellenbosch : Stellenbosch University

Year dc:date.issued

2026

Author dc:creator

• Kyakutwika, Nelson

Advisors dc:contributor.advisor

• Alfeus, Mesias
• Schlogl, Erik
• Bartlett, Bruce

Language dc:language.iso

en

Repository record dc:identifier.uri

https://scholar.sun.ac.za/handle/10019.1/136205

OAI identifier oai:identifier

oai:scholar.sun.ac.za:10019.1/136205