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arXiv · 1509.01175

Correction to Black-Scholes formula due to fractional stochastic volatility

Josselin Garnier·Knut Solna
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Abstract

Empirical studies show that the volatility 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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Josselin Garnier, Knut Solna. 2017-03-19. Correction to Black-Scholes formula due to fractional stochastic volatility. https://arxiv.org/abs/1509.01175

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