# Short-time at-the-money skew and rough fractional volatility

@article{Fukasawa2015ShorttimeAS, title={Short-time at-the-money skew and rough fractional volatility}, author={Masaaki Fukasawa}, journal={Quantitative Finance}, year={2015}, volume={17}, pages={189 - 198} }

The Black–Scholes implied volatility skew at the money of SPX options is known to obey a power law with respect to the time to maturity. We construct a model of the underlying asset price process which is dynamically consistent to the power law. The volatility process of the model is driven by a fractional Brownian motion with Hurst parameter less than half. The fractional Brownian motion is correlated with a Brownian motion which drives the asset price process. We derive an asymptotic…

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