GARCH Volatility Forecasting

Volatility is not constant. It clusters in time — high-vol periods tend to be followed by more high-vol periods, low-vol by more low-vol. GARCH (Generalized Autoregressive Conditional Heteroscedasticity) is the standard model for capturing this clustering and producing forecasts of next-period volatility.

The GARCH(1,1) Specification

The simplest GARCH model is GARCH(1,1):

σ²(t) = ω + α × ε²(t−1) + β × σ²(t−1)

Today's variance is a weighted combination of:

ω (omega): a long-run baseline variance.
α × ε²(t−1): the squared shock from yesterday — captures volatility responses to recent surprises.
β × σ²(t−1): the persistence term — yesterday's volatility carries forward.

Typical empirical estimates for daily equity returns: α ≈ 0.05–0.10, β ≈ 0.85–0.92, with α + β close to (but less than) 1.0. The closer α + β is to 1, the more persistent volatility shocks are; values above 1 indicate explosive volatility (the model is misspecified).

The Half-Life of a Vol Shock

The half-life of a volatility shock — how many bars until its impact decays by half — is approximately −log(2) / log(α + β). For α + β = 0.95, that's about 14 bars. For α + β = 0.99, it's about 69 bars. This is the time scale over which vol shocks propagate.

What GARCH Buys You

Better volatility forecasts than rolling standard deviation. Especially during regime transitions, GARCH adapts much faster than a 30-day rolling σ.
Conditional risk metrics. Daily VaR, expected shortfall, and Sharpe ratio computed using GARCH-conditional variance respond to recent market action.
Volatility-targeted position sizing. If you size to a target σ, GARCH gives you the σ to size against. Smaller positions in high-vol environments, larger in low-vol — automatically.
Better backtests. Bootstrap and Monte Carlo simulations using GARCH-modeled returns capture volatility clustering, producing more realistic stress tests than i.i.d. resampling.

GARCH Variants

EGARCH (Exponential GARCH)

Models the log of variance, allowing for asymmetric volatility responses — negative shocks (drops) often increase volatility more than positive shocks of the same magnitude. The "leverage effect" in equity returns.

GJR-GARCH

An additive way to capture asymmetry: adds a term that activates only on negative shocks. Simpler to interpret than EGARCH.

FIGARCH (Fractionally Integrated GARCH)

Allows for very-long-memory volatility. Useful for daily equity volatility, which exhibits much longer persistence than GARCH(1,1) can fully capture.

For most retail and small-fund applications, GARCH(1,1) with optional GJR asymmetry is sufficient. The diminishing returns from more complex specifications usually don't justify the estimation cost and overfitting risk.

Practical Estimation

GARCH parameters are estimated by maximum likelihood, typically on at least 250 daily observations (one year). Shorter samples produce unreliable parameters.

Once estimated, the model produces:

One-step-ahead variance forecast: what σ² is expected for the next bar.
Multi-step forecast: what σ² is expected several bars ahead, mean-reverting back to the long-run level over the half-life of shocks.
Conditional standardized residuals: the actual return divided by GARCH-implied σ. These should be approximately N(0, 1) if the model fits well.

Failure Modes

Heavy tails. Equity returns have fatter tails than Gaussian. GARCH with Gaussian innovations will under-estimate tail risk; use Student-t or skewed-t innovations for better fit.
Structural breaks. A regime change (2008, 2020) can produce parameter estimates that are "mean values" of two regimes, fitting neither well. Refit before/after structural breaks.
Stale parameters. Parameters drift over years. Use rolling estimation windows for live use.
Overfit by spec selection. Trying many GARCH specifications and picking the best on in-sample fit is the same multiple-testing problem as anywhere else.

Where GARCH Lives in QuanterLab

SC001STCB uses GARCH for two purposes: producing the volatility input to Z-score normalization (so spreads are scaled by their conditional rather than long-run σ), and powering the GARCH Monte Carlo module for forward-looking risk assessment (covered in a separate article).

The Bottom Line

GARCH is the standard tool for "what's the volatility right now and where is it heading?" The math is well-established, the implementations are mature, and the improvement over rolling-window σ is substantial during regime transitions. Use it for any application where conditional volatility matters — sizing, risk metrics, simulation — and stay with the simple GARCH(1,1) variant unless you have a specific reason to elaborate.

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 Heteroscedasticity. Journal of Econometrics, 31(3), 307–327.
Andersen, T. G. & Bollerslev, T. (1998). Answering the Skeptics: Yes, Standard Volatility Models Do Provide Accurate Forecasts. International Economic Review, 39(4), 885–905.

Textbook references

Tsay, R. S. (2010). Analysis of Financial Time Series (3rd ed.). Wiley.
Hamilton, J. D. (1994). Time Series Analysis. Princeton University Press.
Campbell, J. Y., Lo, A. W. & MacKinlay, A. C. (1997). The Econometrics of Financial Markets. Princeton University Press.

Try it in QuanterLab

In SC001STCB enable GARCH-conditional sigma in the OU Z-Score method. Compare the resulting Z-score to a rolling-σ Z-score on a high-vol period — GARCH adapts much faster to vol regime changes, producing more honest entry triggers.