  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.
