Correction to Black--Scholes Formula Due to Fractional Stochastic Volatility

Abstract

Empirical studies show that the volatility process 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.

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