Past exam of the short options paper shared by Prelims and Parts A and B of the physics course of the University of Oxford / 2012 / S9 / 1 / 1 / Solution

Stylized facts of financial returns are robust qualitative statistical regularities found across many instruments or datasets, abstracting from their individual details. Examples include heavy return-distribution tails relative to a Gaussian model, weak linear autocorrelation of many liquid-market returns beyond short lags, and persistent clustering of large absolute or squared returns. Some markets also show asymmetric return-volatility responses and partial movement toward a Gaussian aggregate distribution at longer horizons.

These are empirical tendencies with sampling-scale and market qualifications, not exact universal equations. In particular, weak return autocorrelation does not imply independent increments: volatility clustering and higher-order dependence can remain. A useful model should state which regularities it explains and which its assumptions exclude, rather than treating one convenient random-walk model as an observed law.