The fractional volatility model and rough volatility

The question of the volatility roughness is interpreted in the framework of a data-reconstructed fractional volatility model, where volatility is driven by fractional noise. Some examples are worked out and also, using Malliavin calculus for fractional processes, an option pricing equation and its solution are obtained.
Comment: 13 pages latex, 4 figures. arXiv admin note: text overlap with arXiv:cond-mat/0404684