Rough Bergomi turns grey
Antoine Jacquier, Adriano Oliveri Orioles, Zan Zuric

TL;DR
This paper introduces a new extension of the rough Bergomi model using generalized grey Brownian motion, enabling better calibration of joint SPX/VIX options by relaxing the log-Normal assumption.
Contribution
It proposes a novel model extension that incorporates generalized grey Brownian motion, improving flexibility and calibration for equity options.
Findings
Semi-closed and asymptotic formulas for SPX and VIX options
Numerical evidence of improved calibration performance
Potential advantages over traditional rough Bergomi model
Abstract
We propose a tractable extension of the rough Bergomi model, replacing the fractional Brownian motion with a generalised grey Brownian motion, which we show to be reminiscent of models with stochastic volatility of volatility. This extension breaks away from the log-Normal assumption of rough Bergomi, thereby making it a viable suggestion for the Equity Holy Grail -- the joint SPX/VIX options calibration. For this new (class of) model(s), we provide semi-closed and asymptotic formulae for SPX and VIX options and show numerically its potential advantages as well as calibration results.
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