Before revision:  Inspired by some recent ground-breaking work by Gatheral, Jaisson and Rosenbaum, who showed that fractional Brownian motion with short memory allows for a better calibration of the volatility surface (as opposed to the classical econometric approach of long memory of volatility) , we provide a characterisation of the short- and long-maturity asymptotics of the implied volatility smile.
After revision:  Inspired by some recent ground-breaking work on rough volatility, which showed that models with volatility driven by fractional Brownian motion with short memory allows for a better calibration of the volatility surface (as opposed to the classical econometric approach of long memory of volatility) , we provide a characterisation of the short- and long-maturity asymptotics of the implied volatility smile.