Option pricing under fast-varying long-memory stochastic volatility. (arXiv:1604.00105v1 [q-fin.PR])

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 process and we give the expression for the implied volatility which has a fractional term structure.