by Jim Gatheral, Thibault Jaisson, Mathieu Rosenbaum
Models log-volatility as a rough process with a low Hurst exponent, explains apparent long memory, improves realized-volatility forecasts, and links roughness to high-frequency trading and order splitting.
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Start with the foundations, then use the reading focus to connect the paper to further study.
Follow diffusion-based models and their assumptions.
Separate conditional volatility from observed returns.
Check whether a relationship can be estimated consistently over time.
Read the fitted relationship and its residuals.
Study a correlated stochastic-variance model.
Interpret prices across strikes and expiries.
Study long-run relationships without confusing them with correlation.
Start in discrete time, move to Brownian motion, then read the original pricing argument and simulate it.
Choose a reproducible strategy, specify the trading rule, and test what remains after costs and estimation uncertainty.
Study volatility estimates and risk decisions in a related SMQ project.
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