What it means
Financial markets often show volatility clustering: quiet periods can be followed by more quiet observations, while large movements tend to occur near other large movements. A model assuming one constant variance can miss that pattern.
GARCH allows the variance estimate to update as new observations arrive, rather than treating every period as equally uncertain. The name separates several ideas.
Conditional variance depends on available past information; autoregressive terms use earlier variance estimates; shock terms use squared deviations from the return model. Tim Bollerslev's 1986 paper introduced the generalisation from ARCH, and the additional lagged variance terms can represent persistent volatility without requiring a long list of separate past squared shocks.
A common GARCH(1,1) model uses one lag of the squared shock and one lag of conditional variance, and the two numbers describe the lag structure, not a forecast horizon or a level of confidence. A large recent shock can raise the next variance estimate.
Strong persistence means that the elevated estimate fades slowly unless subsequent information changes the pattern. Variance and volatility are different units: variance is measured in squared return units, while volatility is the square root of variance, making its units comparable with the returns themselves.
The model can help risk teams study potential exposure and update position limits. It can also be used within pricing or portfolio processes, but those applications need additional assumptions and inputs.
Parameter estimates come from data rather than from a universal set of constants, so the sample period, return frequency, mean model and assumed shock distribution can affect the resulting forecast. A plain symmetric GARCH model responds to equal-sized positive and negative shocks through their squares.
Other models allow asymmetric reactions, which can matter where falling prices are associated with stronger volatility changes. Check out-of-sample behaviour rather than only historical fit, because a complicated model can describe the training data well and still fail during a new regime, market closure or unusual event.
For a manager, ask what the forecast measures and what decisions it supports. A volatility number should be accompanied by its horizon, units, assumptions and limitations, not presented as a precise prediction of tomorrow's profit or loss.
In practice
Real-world examples.
Example
An asset has several large daily moves after a quiet month. A GARCH forecast can rise as new shocks enter the model, recognising that near-term uncertainty may differ from the earlier calm period.
Example
Two price series have the same average return but different volatility persistence. A risk manager can use changing variance estimates to compare potential short-term exposures without claiming that either series will rise next.
Example
A report prints a variance of 0.0001 for decimal daily returns. Taking the square root gives 0.01, or 1% daily volatility. Calling the variance itself '1% volatility' would confuse both units and magnitude.
Formula
Calculation
A basic model is h(t) = omega + alpha times e(t-1)^2 + beta times h(t-1). With omega 0.000002, alpha 0.10, beta 0.85, a previous shock 0.02 and previous variance 0.0001, the next variance is 0.000127.
Its square root is approximately 1.13% when returns use decimal units. These illustrative parameters are not recommended estimates for any asset.Case study
Seen in the real world.
Fictional case study: Crescent Trading used a GARCH dashboard to adjust daily risk limits. A manager saw a low forecast after several quiet weeks and treated it as evidence that a large position could not lose much. An unexpected policy announcement caused a sharp movement beyond the recent pattern.
The updated model raised volatility afterward, but it had not guaranteed that such a shock would be absent beforehand. Crescent retained the model as one input and added stress scenarios, concentration limits and a cash plan. Its reports separated statistical forecasts from extreme-event tests, recognising that estimated conditional variance is useful information but not a ceiling on loss.
Watch out
Common mistakes.
- Using a volatility forecast as a directional price signal. A higher variance estimate does not say whether the next return will be positive or negative.
- Confusing variance, volatility and annualisation. Record return units and observation frequency before comparing outputs or scaling them.
- Assuming historical fit proves future reliability. Regime changes, data problems and model assumptions can make a well-fitted forecast misleading.
Questions
People also ask.
Is GARCH the same as ARCH?
No. GARCH extends ARCH by including earlier conditional variances as well as past squared shocks, allowing a different representation of volatility persistence.
Does GARCH forecast the asset's price?
Its main role is modelling conditional variance. A separate return or pricing model is needed, and neither component guarantees a realised outcome.
What should a non-specialist check in a report?
Ask for the forecast horizon, units, data period, model version and stress tests. Confirm how the estimate changes the decision instead of accepting a number without context.
From the founder's library
Take it further with the book.
Build your financial confidence beyond this definition. Shihan's full-length guide, Accounting Fundamentals, takes the same plain-English approach and turns it into a complete, practical playbook for non-finance managers, business owners and students - with chapter-end quiz answers and presentation slides included.
25% off with code MMHQ25, applied at checkout. Priced in USD - checkout may show the equivalent in your local currency.
View the book and save 25%