GARCH ModelGARCH
A GARCH model is a statistical model of volatility that changes over time, in which today’s volatility depends on recent shocks and recent volatility. It captures volatility clustering and is widely used in risk models.
A GARCH model forecasts volatility by letting it change with recent shocks and its own past level. It is a workhorse of risk management because market calm and turbulence tend to come in clusters.
- Category
- Indicators and Tools
- Reading time
- 3 min
- Also called
- Generalized ARCH, GARCH(1,1)
- Updated
GARCH in plain words
Volatility changes over time: big moves tend to follow big moves, and calm tends to follow calm.1
Engle’s graduate student Tim Bollerslev introduced the generalized ARCH (GARCH) model to capture this.1
GARCH captures that clustering, the drift of volatility back to normal, and how long shocks linger.2
How GARCH(1,1) works
Get returns
Compute daily percentage returns and remove the average.
Set the structure
GARCH(1,1) distills volatility dynamics into three fundamental parameters.2
Shock term
Read α as how strongly today's move feeds into tomorrow's expected volatility.2
Persistence term
Read β as how slowly a volatility shock fades — it sets the shock's half-life.2
Long-run level
Volatility converges toward ω / ( 1 - α - β ).2
Forecast and check
Estimate parameters, forecast variance and test the fit out of sample.
Worked examples
Example 1 — One-step forecast
Variance 2.12Hypothetical ω 0.02, α 0.10, β 0.85; yesterday’s squared return 4 and variance 2.
| ω | 0.02 |
| α × 4 | 0.40 |
| β × 2 | 1.70 |
| Forecast variance | 2.12 |
Today’s variance depends on the latest shock (α) and past variance (β), the parameters V-Lab describes.2
Example 2 — Long-run level
Mean revertsWith the same hypothetical ω 0.02, α 0.10, β 0.85.
| 1 − α − β | 0.05 |
| Long-run variance | 0.40 |
Using ω / ( 1 - α - β ), variance reverts toward 0.40.2
Example 3 — High persistence
Slow decayA hypothetical model has β 0.95.
| β | 0.95 |
High β means shocks fade slowly, since β sets the half-life of volatility shocks.2
GARCH vs historical volatility
| Aspect | GARCH | Historical volatility |
|---|---|---|
| Weights | Recent shocks weigh more | Equal weights |
| Mean reversion | Built in | None |
| Forecasting | Designed for it | Backward-looking |
| Complexity | Needs estimation | Simple |
Where GARCH is used
Risk models
Feeds Value at Risk estimates.
Options
Compare with Implied Volatility.
Position sizing
Scale Position Sizing to forecast Volatility.
Research
Model volatility in Backtesting.
Advantages and disadvantages
Advantages
- Captures volatility clustering.
- Few parameters.
- Mean reverting forecasts.
- Widely supported in software.
Disadvantages
- Assumes a fixed structure.
- Struggles with sudden jumps.
- Basic version treats up and down shocks alike.
- Estimates can be unstable.
Going deeper
Read as far as you need. Each level builds on the one before it.
History
Beginner
Parameters
Intermediate
V-Lab describes α as shock sensitivity and β as setting the half-life of shocks; together they determine how quickly volatility returns to its long-run level.2
Practice
Advanced
ARCH-type models are now standard tools in financial analysis.1 Many variants add asymmetry or fat tails.
Common mistakes
Ignoring α + β near 1
Very high persistence makes forecasts slow to revert.
Using prices, not returns
Model returns.
Trusting one fit
Re-estimate and test.
Ignoring fat tails
Normal errors understate extremes.
Check your understanding
Test yourself before moving on. Each answer comes with an explanation.
Key points to remember
- GARCH models time-varying volatility.
- It captures volatility clustering.
- α measures shock impact, β persistence.
- Volatility reverts to a long-run level.
- It is widely used in risk models.
Frequently asked questions
What does (1,1) mean?
Who created GARCH?
Does GARCH predict direction?
Further learning
- Volatility
What GARCH models.
- Value at Risk
Risk use.
- Implied Volatility
Market-based view.
- Mean Reversion
Why forecasts revert.
Sources
This article is written in our own words. The sources below support the specific facts, rules and figures marked with a number in the text. Links open the original publisher’s page.
- The Royal Swedish Academy of Sciences (Nobel Prize). Time-series Econometrics: Cointegration and ARCH (2003 advanced information) (opens in a new tab) Checked .
- NYU Stern V-Lab. GARCH Volatility Documentation (opens in a new tab) Checked .
Educational content, not financial advice. Examples use hypothetical prices and simplified costs; actual fees, margin rules and regulations vary by broker, market and country. We are not affiliated with any publisher linked above. Last reviewed . Report an error or request a source credit.