Long memory stochastic volatility (LMSV) models have been used to explain the persistence of volatility in the market, while rough stochastic volatility (RSV) models have been shown to reproduce statistical properties of high frequency financial data. In these two classes of models, the volatility process is often described by a fractional Ornstein-Uhlenbeck process with Hurst index H, where H>1/2 for LMSV models and H<1/2 for RSV models. The goal of this talk is to discuss recent advances in option pricing, parameter estimation and hedging under fractional stochastic volatility models.
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