GARCH Risk Statistics
- FX
The risk-statistics portion of FE-635 introduces GARCH as a way to model time-varying volatility. Returns may have little serial correlation while their squared returns cluster: calm periods tend to be followed by calm periods, and shocks tend to persist.
A simple GARCH(1,1) recurrence is
$$\sigma_t^2=\omega+\alpha\epsilon_{t-1}^2+\beta\sigma_{t-1}^2.$$
The parameters describe long-run variance, reaction to a new shock, and persistence. Estimation and diagnostics matter as much as the recurrence; a fitted model should be checked against the horizon and the tail behavior of the risk report.