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 by Gatheral, Jaisson and Rosenbaum, who showed that fractional Brownian motion with short memory allows for 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.