Rough Bergomi turns grey

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.