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}
}
  • M. Fukasawa
  • Published 27 January 2015
  • Mathematics, Economics
  • Quantitative Finance
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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