  Recent empirical studies suggest that the volatility of an underlying price
process may have correlations that decay slowly under certain market
conditions. In this paper, the volatility is modeled as a stationary process
with long-range correlation properties in order to capture such a situation,
and we consider European option pricing. This means that the volatility process
is neither a Markov process nor a martingale. However, by exploiting the fact
that the price process is still a semimartingale and accordingly using the
martingale method, we can obtain an analytical expression for the option price
in the regime where the volatility process is fast mean-reverting. The
volatility process is modeled as a smooth and bounded function of a fractional
Ornstein-Uhlenbeck process. We give the expression for the implied volatility,
which has a fractional term structure.
