What it means
Markets do not move at a steady pace. A quiet month is often followed by another quiet month, and a violent week tends to be followed by more violent weeks, a pattern known as volatility clustering.
A simple standard deviation over a long period treats every day alike, so it reacts slowly when conditions change. GARCH fixes this by letting the forecast adjust each day.
In its most common form, called GARCH(1,1), the next variance (volatility squared) is built from three parts: a small long-run baseline, yesterday's surprise move, and yesterday's variance forecast. A big surprise pushes the forecast up, and calm days let it drift back down.
The name unpacks neatly. Autoregressive means the series depends on its own past, conditional means the forecast uses what is known today, and heteroskedasticity is the statistical word for variance that changes over time.
The word generalised refers to the extension of an earlier model, ARCH, that added the previous forecast as an input. In business, the forecast feeds directly into decisions.
Banks use it for Value at Risk (an estimate of the most a portfolio might lose on a normal bad day), traders use it to compare model volatility with option prices, and treasury teams use it to decide how much currency exposure to hedge. Anyone sizing a position to a fixed risk budget can divide the budget by the forecast volatility.
There are limits to bear in mind. The parameters must be estimated from data, so poor data or a short window gives unreliable output.
GARCH forecasts the size of moves, not their direction, and the forecast drifts back towards the long-run level over time rather than staying high forever.
In practice
Real-world examples.
Example
A bank risk desk updates its daily Value at Risk each morning using a GARCH forecast. After a volatile week, the forecast for a $50,000,000 portfolio rises to about 1.11% a day, so a one-standard-deviation daily move is roughly $555,000, and the desk trims its limits.
Example
An options trading firm compares its GARCH forecast of an equity index with the volatility implied by option prices. When options look expensive relative to the forecast, the firm sells them; when they look cheap, it buys.
Example
The treasury team of an importer with large euro payables watches its currency volatility forecast. When the forecast jumps, the team raises its hedge ratio (the share of exposure protected) from 50% to 75% for the coming quarter.
Formula
Calculation
GARCH(1,1): next variance = omega + alpha x (yesterday's shock squared) + beta x (yesterday's variance)
Assume omega = 0.000002, alpha = 0.08 and beta = 0.90. Yesterday's forecast volatility was 1% a day, so yesterday's variance was 0.0001. Yesterday's return surprise was 2%, so the shock squared was 0.02 x 0.02 = 0.0004. Next variance = 0.000002 + (0.08 x 0.0004) + (0.90 x 0.0001) = 0.000002 + 0.000032 + 0.00009 = 0.000124. The square root of 0.000124 is about 0.0111, so tomorrow's forecast volatility is about 1.11%. On a $1,000,000 portfolio, a typical one-standard-deviation daily move is about $11,100. The long-run variance is omega / (1 - alpha - beta) = 0.000002 / 0.02 = 0.0001, which is 1% a day.Case study
Seen in the real world.
Redwater Asset Partners is an illustrative, fictional fund that targets a risk of $10,000 per day on each strategy. The risk team divides that budget by the forecast daily volatility to decide how large each position should be.
With volatility at 1.00%, the position was $10,000 / 0.01 = $1,000,000. After a sharp market shock, the GARCH forecast rose to about 1.11%, and the model automatically cut the position to roughly $900,000, without anyone having to make a judgement call in a stressful moment.
The managing partner liked that the rule was written down in advance. The illustrative lesson is that a volatility model works best as a discipline that scales risk up and down, not as a crystal ball.
Watch out
Common mistakes.
- Believing GARCH predicts whether prices will rise or fall, when it only forecasts how large the moves are likely to be.
- Fitting the model to a very short or poor-quality price history and trusting the output as if it were precise.
- Assuming a high volatility forecast will stay high, when the model pulls it back towards the long-run level.
Questions
People also ask.
What does GARCH(1,1) mean?
It means the model uses one lagged shock and one lagged variance forecast, which is the most widely used and simplest version.
Why not just use a standard deviation?
A plain standard deviation weights every past day equally, whereas GARCH reacts faster to recent turbulence and then fades it gradually.
Do non-quants need to run the model?
No, but managers who rely on risk figures should know that a model like this sits behind them, along with its assumptions.
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