What is a GARCH model?
A GARCH (Generalized AutoRegressive Conditional Heteroskedasticity) model holds that the variance of a series changes over time and depends on past shocks and past variance. Robert Engle introduced ARCH in 1982 while modeling UK inflation, and his student Tim Bollerslev generalized it in 1986. Engle shared the 2003 Nobel Prize in economics for this work.
- Problem
- Volatility clustering
- ARCH
- Variance from past squared shocks
- GARCH
- Past shocks + past variance
- Workhorse
- GARCH(1,1)
Volatility clustering
Plot daily stock returns and calm and turbulent periods come in clumps: volatility clustering. An ARIMA model assumes constant variance and misses this.
The intuition of GARCH(1,1)
Today's variance = long-run level + α × (yesterday's shock)² + β × (yesterday's variance)
α captures sensitivity to news; β captures persistence. In equity data α+β is often close to 1, so shocks fade slowly.
Why do markets keep swinging for days in a crisis? One large shock keeps investors anxious and volatility stays high. GARCH quantifies this "turbulence breeds turbulence" pattern.
Uses
- Risk management and value at risk (VaR)
- Volatility forecasts for option pricing
- Time-varying portfolio risk
- Exchange-rate and commodity volatility
Limitations
The basic model treats good and bad news symmetrically, but falling prices tend to raise volatility more, which led to asymmetric models such as EGARCH and GJR-GARCH. The broader question of predictability relates to the efficient market hypothesis.
Frequently asked questions
- ARCH vs GARCH?
- ARCH uses only past shocks; GARCH adds past variance, capturing persistence with fewer parameters.
- Why GARCH(1,1)?
- It is parsimonious and fits most financial data well.
- Does GARCH predict price direction?
- No. It forecasts the size of volatility, not direction.
References
- Engle, R. F. (1982). Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation. Econometrica, 50(4), 987–1007.
- Bollerslev, T. (1986). Generalized autoregressive conditional heteroskedasticity. Journal of Econometrics, 31(3), 307–327.