Rough volatility

Quantitative Finance Glossary

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.

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