Pricing and Calibration of VIX Derivatives in Mixed Bergomi Models via Quantisation

TL;DR

This paper introduces a fast, efficient vector quantisation method for pricing and calibrating mixed Bergomi models to VIX derivatives, demonstrating high accuracy and stability over extensive market data.

Contribution

It presents a novel application of vector quantisation for efficient calibration of mixed Bergomi models to VIX market data.

Findings

Models fit VIX derivatives accurately.

Calibration is feasible over several months of data.

Parameters remain stable over time.

Abstract

We apply vector quantisation within mixed one- and two-factor Bergomi models to implement a fast and efficient approach for option pricing in these models. This allows us to calibrate such models to market data of VIX futures and options. Our numerical tests confirm the efficacy of vector quantisation, making calibration feasible over daily data covering several months. This permits us to evaluate the calibration accuracy and the stability of the calibrated parameters, and we provide a comprehensive assessment of the two models. Both models show excellent performance in fitting VIX derivatives, and their parameters show satisfactory stability over time.