Markets Get Volatile in Clusters. GARCH Knows This and Uses It.
One of the most consistent patterns in financial markets is that volatility clusters. Big moves tend to be followed by more big moves; calm periods tend to stay calm. This is not a subtle effect; you can see it clearly in any chart of daily returns. The enormous swings of March 2020 did not appear out of nowhere in an otherwise quiet year. They arrived in clusters, one wild day followed by another, before eventually settling back down.
Standard models like ARIMA assume that the variance of errors is constant over time. In financial data, that assumption is badly wrong. Variance in markets is highly persistent and predictable; knowing how volatile the market was yesterday tells you a lot about how volatile it will be tomorrow.
GARCH, which stands for Generalized Autoregressive Conditional Heteroskedasticity (yes, economists name things to intimidate people), was developed specifically to model this behavior. It treats volatility itself as something that evolves over time and can be forecast.
The FatNarwhal GARCH tool fits a GARCH model to any stock's return series and gives you the conditional volatility forecast; how volatile the model expects the next period to be based on recent history.
How to Use It
Go to fatnarwhal.com/garch and enter a ticker.
The tool fits a GARCH(1,1) model to the daily returns of that stock and plots two things; the historical conditional volatility (how volatile the model thinks each past period was, using only information available at the time), and the forward volatility forecast.
High spikes in the historical conditional volatility plot correspond to periods of market stress; you will see them clearly around events like the 2020 COVID crash, the 2022 rate shock, and any major geopolitical event. The model shows how quickly volatility reverted toward its long-run average after each spike.
The forward forecast shows where the model thinks volatility is headed based on the current state. If you are coming off a high-volatility period, the model will predict elevated volatility for the near future before gradually mean-reverting. If volatility has been low, it forecasts that it will stay low, with some small upward drift toward the long-run average.
The Math Behind It
GARCH(1,1) models the variance (σ²) of returns at time t as:
Where ω is a long-run variance constant, ε²_(t-1) is the squared return shock from yesterday (how big yesterday's actual surprise was), and σ²_(t-1) is yesterday's conditional variance.
The α parameter captures how strongly yesterday's shock affects today's variance; it governs the spikiness of the volatility process. The β parameter captures persistence; how much yesterday's variance carries forward into today. In practice for equity markets, β is usually large (around 0.85 to 0.95) and α is smaller (around 0.05 to 0.15), which reflects the fact that volatility is very persistent and responds somewhat but not enormously to individual return shocks.
The long-run average variance implied by the model is ω / (1 − α − β). When α + β is close to 1, volatility is highly persistent and slow to revert; when it is further below 1, volatility reverts toward its mean more quickly.
When to Use It and When Not To
GARCH is particularly useful for options traders who want a model-based estimate of forward volatility to compare against implied volatility. If the GARCH forecast is significantly below the implied vol in the options market, that is a signal that options might be expensive relative to what the time series model expects. If GARCH vol is above implied vol, options might be cheap.
It is also useful for risk management; knowing whether you are in a high-volatility or low-volatility regime matters for position sizing and stop levels.
GARCH is less useful in a few scenarios. During fundamental regime changes (a new monetary policy era, a structural shift in market microstructure) the historical parameters may not describe the new environment well. And GARCH tells you about the volatility of the asset's own returns; it does not model correlations between assets changing over time, which is a separate problem.
Try It
Run the GARCH tool on any stock at fatnarwhal.com/garch during or right after a period of elevated market volatility. Look at the conditional volatility plot and the forward forecast. Compare the current volatility estimate against the long-run average the model implies. That ratio tells you where you are in the volatility cycle and gives you a grounded starting point for options decisions or risk management.
Markets cluster. GARCH pays attention.