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 log-normal: 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 term-structure of volatilities of volatilities, and consider its calibration to the VIX market.