Speaker: Mathieu Rosenbaum, École Polytechnique
It has been recently shown that rough volatility models, where the volatility is driven by a fractional Brownian motion with small Hurst parameter, provide very relevant dynamics in order to reproduce the behavior of both historical and implied volatilities. However, due to the non-Markovian nature of the fractional Brownian motion, they raise new issues when it comes to the risk management of derivatives. Using an original link between nearly unstable Hawkes processes and rough volatility models, we explain in this talk how to price and hedge options in the rough version of the Heston model. This is joint work with Omar El Euch.