The fractional volatility model: No-arbitrage, leverage and completeness
  Based on a criterion of mathematical simplicity and consistency with empirical market data, a stochastic volatility model has been obtained with the volatility process driven by fractional noise. Depending on whether the stochasticity generators of log-price and volatility are independent or are the same, two versions of the model are obtained with different leverage behavior. Here, the no-arbitrage and completeness properties of the models are studied. 
R. Vilela Mendes, M. J. Oliveira and A.M. Rodrigues
q-fin.ST