Rough Volatility

Gatheral et al. (2018): realized volatility is log-fractional Brownian motion with Hurst exponent H ≈ 0.1 — far rougher than Brownian motion (H=0.5). Rough volatility explains the steep implied volatility skew observed in equity options markets.

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Top: Log-price path | Middle: Log-volatility (fBm) | Bottom: Implied vol skew comparison