Abstract:
Recently proposed models for the forward variance and the spot value of the SP500 based on fractional Volterra processes – more specifically, the 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 directions, building on the work of Bergomi [2008, 2016], to overcome this limitation.