What Is a GARCH Model? Forecasting Market Volatility

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GARCH (Generalized AutoRegressive Conditional Heteroskedasticity) is a statistical model that forecasts the volatility of a financial return series by letting today’s variance depend on recent squared surprises and on yesterday’s variance. A GARCH model treats volatility as something that changes over time and clusters: turbulent days tend to follow turbulent days, and calm periods tend to persist.

What Heteroskedasticity Means Here

Most regression and time-series models assume the error term has a constant variance, a property called homoskedasticity. Financial returns rarely behave that way. Their variance shifts, and large moves bunch together in time. That irregular variance is heteroskedasticity.

“Conditional” heteroskedasticity adds a specific claim: the variance at any point depends on past information. In GARCH, the error term’s variance follows an autoregressive moving average pattern, so it is a function of its own past values and of past squared errors. A model that ignores this and assumes constant variance will understate risk during volatile stretches and overstate it during quiet ones, and its forecasts lose reliability.

How a GARCH Model Works

The most widely used specification is GARCH(1,1), which uses one lag of each input:

σ²ₜ = ω + α·ε²ₜ₋₁ + β·σ²ₜ₋₁

• σ²ₜ is the conditional variance forecast for period t.
• ω (omega) is a constant that anchors the long-run level.
• α (alpha) weights yesterday’s squared shock, ε²ₜ₋₁, the “news” term.
• β (beta) weights yesterday’s variance forecast, the “memory” term.

The parameters are usually estimated by maximum likelihood, commonly assuming normally distributed or Student’s t shocks. For the model to be stationary, ω must be positive, α and β non-negative, and α + β below 1.

Interpreting the Parameters

α + β measures persistence. Values close to 1 mean a volatility shock fades slowly. The model also implies a long-run variance of ω / (1 − α − β), the level toward which forecasts drift as the horizon lengthens. A high α relative to β produces a jumpy volatility estimate that reacts sharply to each day’s move; a high β produces a smoother estimate that changes gradually.

Example of a GARCH Model

Hypothetical parameters for illustration only, not estimated from any market. Suppose a currency pair’s daily returns are fitted with:

• ω = 0.000002, α = 0.08, β = 0.90
• Yesterday’s variance forecast: 0.0001 (a 1% daily volatility)
• Yesterday’s return surprise: −2%, so ε² = 0.0004

Today’s variance:

0.000002 + 0.08 × 0.0004 + 0.90 × 0.0001 = 0.000124

The square root gives a daily volatility forecast of about 1.11%, up from 1% because yesterday’s move was twice the expected size. Annualized with 252 trading days, that is roughly 17.7%.

Persistence here is 0.98, and the long-run variance is 0.000002 / 0.02 = 0.0001, or 1% daily. With persistence of 0.98, a shock’s effect on variance halves in about 34 trading days (ln 0.5 / ln 0.98). If the same −2% move had been a +2% move, the forecast would be identical, because the shock enters squared.

What the GARCH Model Is Used For

GARCH can be applied to macroeconomic series, but its main use is estimating the volatility of stocks, bonds, currencies, commodities and market indices. Common applications:

• Value-at-Risk (VaR). A VaR-GARCH approach feeds the conditional volatility forecast into a VaR calculation, the maximum expected loss over a set period at a given confidence level, for a position, portfolio, division or whole firm. Using the example above and assuming normally distributed returns with a zero mean, a one-day 95% VaR is 1.645 × 1.11% ≈ 1.83%, or about $1,830 on a $100,000 position. Because the volatility input updates daily, the risk estimate widens after shocks instead of relying on a single long-run standard deviation.
• Position sizing and stops. Traders scale exposure to forecast volatility, sizing smaller when σ rises. A position size calculator handles the lot math once a volatility-based stop distance is chosen.
• Hedging and allocation. Multivariate versions estimate changing correlations, used for hedge ratios and portfolio optimization. See how hedging works.
• Option pricing. Volatility forecasts serve as an input for pricing and for comparing against implied volatility.

GARCH Variants

The original model captures magnitude but not direction. Later variants address that and other features:

• GJR-GARCH and EGARCH let negative shocks raise volatility more than positive shocks of the same size (the “leverage effect” seen in equities).
• NGARCH (Nonlinear GARCH) adds nonlinearity to how shocks feed volatility clustering.
• IGARCH (Integrated GARCH) restricts α + β to exactly 1, so shocks never fade; the long-run variance is then undefined, a known drawback.
• GARCH-M adds the variance into the return equation, so expected return depends on risk.
• SARIMA-GARCH pairs a seasonal ARIMA model for the mean with GARCH errors.

GARCH vs. ARCH and Other Volatility Measures

ARCH models variance using only past squared shocks. Capturing long memory requires many lags and parameters. GARCH adds lagged variance, so one term summarizes the entire past, which is why GARCH(1,1) often replaces a long ARCH specification.

Historical volatility is a plain standard deviation over a window, with every day weighted equally and nothing forecast. Implied volatility is backed out of option prices and reflects market expectations rather than a statistical fit. GARCH sits between them: it is backward-looking in its inputs but produces an explicit forecast.

Limitations of a GARCH Model

• Distribution assumptions. Normal shocks understate fat tails and asymmetry; see skewness and the bell curve for why that matters.
• Symmetric response in the standard version.
• Parameter instability. Estimates fitted in calm periods can perform poorly after structural breaks, and researchers have studied how reliably GARCH variants held up around the Great Recession.
• Mean reversion assumption. Forecasts always drift toward the long-run level, which may lag a genuine regime change.
• Intraday data contains time-of-day patterns and microstructure noise that a plain GARCH fit does not handle without adjustments.

GARCH forecasts the size of future moves, not their direction, so it informs risk rather than generating trade signals on its own.

FAQs

The Bottom Line

GARCH matters to risk managers, quantitative traders and anyone sizing positions, hedging or pricing options, because it updates volatility forecasts as new shocks arrive. Use it to estimate how large future moves may be, and pair it with a fat-tailed distribution or an asymmetric variant when losses and extreme moves matter. It forecasts the size of moves, not their direction, so it supports risk decisions rather than producing trade signals.