Rough volatility
Quantitative Finance glossary · Derivatives Pricing & Volatility Surfaces
Definition
Volatility models driven by fractional Brownian motion B_t^H with Hurst exponent H < 1/2 — typically H in (0.05, 0.15), far rougher than standard BM (H = 1/2). The rough Bergomi model and rough Heston explain the empirical short-dated power-law explosion of ATM skew (partial σ_imp / partial ln K propto T^H - 1/2) that classical stochastic-vol cannot. Non-Markovian — pricing requires Monte Carlo or Volterra-PDE methods. The dominant academic-frontier vol-modelling paradigm post-2014.
Rough volatility in plain English
"Volatility" is how jumpy a price is, and it isn't constant — it itself wiggles over time. Rough volatility is the discovery that this wiggling is far *jaggeder* than older models assumed: instead of the smooth-ish randomness of a normal random walk, it uses a rougher kind (fractional Brownian motion with a "Hurst exponent" H around 0.1, versus the standard H = 1/2) — think a coastline zoomed in, spiky at every scale rather than gently curved. This roughness matters because it correctly reproduces something real markets show that smoother models miss: the way short-dated options' pricing behavior explodes as expiration nears. It's harder to compute (you usually need simulation), but since about 2014 it's been the hottest frontier in academic volatility modeling.
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