FRM Glossary · Part I · Quantitative

ARCH / GARCH

Time-series models that let volatility cluster — conditional variance is a function of past squared returns (ARCH) and past variance (GARCH).

In more detail

An ARCH(p) model writes σ²_t = ω + Σ αᵢ r²_{t−i}. GARCH(p,q) adds lagged variance terms σ²_{t−j}. GARCH(1,1) with ω + α + β < 1 is the workhorse model in FX, equity, and rates volatility forecasting. The integrated-GARCH (IGARCH), GJR-GARCH (asymmetric leverage), and exponential-GARCH variants capture additional stylised facts.