A data-reconstructed fractional volatility model
  Based on criteria of mathematical simplicity and consistency with empirical market data, a stochastic volatility model is constructed, the volatility process being driven by fractional noise. Price return statistics and asymptotic behavior are derived from the model and compared with data. Deviations from Black-Scholes and a new option pricing formula are also obtained 
Rui Vilela Mendes and M. J. Oliveira