VIX derivatives in rough forward variance models

Recently proposed models for the forward variance and the spot value of the SP500 based on fractional Volterra processes - specifically, the so called rough Bergomi model of [Bayer, Gatheral, Friz 2016] - are not able to... [ view full abstract ]

Recently proposed models for the forward variance and the spot value of the SP500 based on fractional Volterra processes - specifically, the so called rough Bergomi model of [Bayer, Gatheral, Friz 2016] - are not able to account for smiles of options on VIX (the major implied volatility index on the SP500). Indeed, the VIX process induced by this model is essentially log-normal: any calibration to the VIX market instruments is, then, out of reach. We will discuss solutions, building on the work of Bergomi [2008,2016], to overcome this limitation.