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.
\nA simple GARCH(1,1) recurrence is
\n$$\\sigma_t^2=\\omega+\\alpha\\epsilon_{t-1}^2+\\beta\\sigma_{t-1}^2.$$
\nThe 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.
","contentMarkdown":"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.\n\nA simple GARCH(1,1) recurrence is\n\n$$\\sigma_t^2=\\omega+\\alpha\\epsilon_{t-1}^2+\\beta\\sigma_{t-1}^2.$$\n\nThe 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.","dataUrl":"https://sharifhsn.dev/api/posts/garch-risk-statistics.json","date":"2025-03-24","datePublished":"2025-03-24","description":"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: ca…","site":"https://sharifhsn.dev","slug":"garch-risk-statistics","source":"FE-635 | Risk Engineering","sourceUrl":null,"tags":["FX","GARCH","Volatility Estimation"],"title":"GARCH Risk Statistics","url":"https://sharifhsn.dev/blog/garch-risk-statistics/","version":"1","wordCount":83}