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

Option pricing under fast-varying long-memory stochastic volatility