Correction to Black-Scholes Formula Due to Fractional Stochastic Volatility

@article{Garnier2017CorrectionTB,
  title={Correction to Black-Scholes Formula Due to Fractional Stochastic Volatility},
  author={Josselin Garnier and Knut S\olna},
  journal={SIAM J. Financial Math.},
  year={2017},
  volume={8},
  pages={560-588}
}
Empirical studies show that the volatility may exhibit correlations that decay as a fractional power of the time offset. The paper presents a rigorous analysis for the case when the stationary stochastic volatility model is constructed in terms of a fractional Ornstein Uhlenbeck process to have such correlations. It is shown how the associated implied volatility has a term structure that is a function of maturity to a fractional power. 

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