GARCH

Quantitative Finance Glossary

Generalised AutoRegressive Conditional Heteroskedasticity — model of time-varying conditional variance. GARCH(1,1): σ_t^2 = ω + α,varepsilon_t-1^2 + β,σ_t-1^2, with stationarity α + β < 1. Captures volatility clustering (ρ(varepsilon_t^2, varepsilon_t-1^2) > 0) and mean-reverting volatility, but symmetric in shocks; GJR-GARCH and EGARCH add the leverage effect (negative shocks raise vol more than positive). The unconditional variance is ω/(1-α-β).

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