Hurst Exponent & Rough Paths: Stochastic Toolkit for Rough Bergomi (Ep.2)

aster the stochastic toolkit behind rough volatility: Markov vs non-Markov, Brownian vs fractional Brownian motion, the Hurst exponent H ≈ 0.1, rough Bergomi parameters, and the implied volatility surface. Episode 2 of my thesis study series (Chapter 2a). Intuition-first deep dive for quantitative finance and data science students preparing a viva—not a measure-theory lecture. What you’ll learn • Markov property and why it unlocks PDE / Feynman–Kač shortcuts • Standard Brownian motion (4 properties) vs fractional Brownian motion • Hurst exponent H: smooth vs rough paths; why market volatility looks rough • Rough Bergomi parameters {H, η, ξ₀, ρ} in plain English • Implied volatility surfaces, smile/skew, and no-arbitrage (calendar & butterfly) • Why Monte Carlo calibration is expensive • Why classical Feynman–Kač fails—and why BSDEs enter the picture Series: Rough Volatility Calibration with Physics-Informed Neural Networks Episode 2 of 7 · Chapter 2a — Stochastic foundations Next: Ep.3 — PINNs, BSDEs & the unsupervised neural calibration loop Topics: Hurst exponent, fractional Brownian motion, rough Bergomi, implied volatility surface, Monte Carlo simulation, Feynman-Kac, BSDE, quantitative finance, stochastic volatility #HurstExponent #RoughVolatility #RoughBergomi #QuantitativeFinance #StochasticCalculus