The scaling properties of historical volatility time series, which now appear to be universal, motivate the modeling of volatility as the exponential of fractional Brownian motion. This model can be understood as reflecting the high endogeneity of liquid markets and the long memory of order flow. The Rough Bergomi model which is the simplest corresponding model under Q fits the implied volatility surface remarkably well. As an application, we show how to forecast the variance swap curve. We also present a quasi-explicit expression for the characteristic function of a natural fractional generalization of the Heston model, a model which also fits the volatility surface very well, in contrast to the classical Heston model. Finally, we comment on the calibration of rough volatility models, which is still work in progress.
5:00 p.m. Tea, VinH 120
5:30 - 6:30 p.m., VinH 16