Rough volatility: An overview by Jim Gatheral

Presentation at the LSE Risk and Stochastics Conference 2017 by Jim Gatheral, Baruch College.

Abstract: 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 comment in detail on model calibration, which turns out not to be straightforward.