Before revision:  The volatility process is here modeled as a smooth and bounded function of a fractional Ornstein Uhlenbeck processand we give the expression for the implied volatility  which has a fractional term structure.
After revision:  The volatility process is here modeled as a smooth and bounded function of a fractional Ornstein Uhlenbeck processand we give the expression for the implied volatility , which has a fractional term structure.