VIX derivatives in rough forward variance models by Stefano De Marco

Presentation at the LSE Risk and Stochastics Conference 2018 by Stefano De Marco, École Polythechnique. Recently proposed models for the forward variance and the spot value of the SP500 stock index based on fractional Volterra processes specifically, the so called rough Bergomi model of Bayer, Friz, Gatheral 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 lognormal: any calibration to the VIX market instruments is, then, out of reach. We will focus on the pricing and hedging of volatility derivatives, and on the appealing features that such an extended rough modeling framework possesses in the termstructure of volatilities of volatilities, and consider its calibration to the VIX