On VIX Futures in the Rough Bergomi Model

Abstract

The rough Bergomi model introduced by Bayer, Friz and Gatheral has been outperforming conventional Markovian stochastic volatility models by reproducing implied volatility smiles in a very realistic manner, in particular for short maturities. We investigate here the dynamics of the VIX and the forward variance curve generated by this model, and develop efficient pricing algorithms for VIX futures and options. We further analyse the validity of the rough Bergomi model to jointly describe the VIX and the SPX, and present a joint calibration algorithm based on the hybrid scheme by Bennedsen, Lunde and Pakkanen.

Keywords: Implied volatility, fractional Brownian motion, rough Bergomi, VIX Futures, VIX smile

JEL Classification: G20, G99, G60, B25