Recent empirical studies suggest that the volatility of an underlying price process may have correlations that decay relatively slowly under certain market conditions. In this paper, the volatility is modeled as a stationary process with long-range correlation properties  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 still is a semimartingale and accordingly using the martingale method, one can get an analytical expression for the option price in the regime when the volatility process is fast mean reverting . 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.
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.
D
relatively
A
in order
A
,
R
still is
is still
R
one can get
we can obtain
R
when
where
R
mean reverting
mean-reverting
D
here
R
Ornstein Uhlenbeck processand we
Ornstein-Uhlenbeck process. We
A
,