  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.
