GARCH — modelling volatility

If returns are nearly unpredictable, volatility is not. Volatility clusters: big moves follow big moves. That predictable structure is what GARCH models capture, and it is one of the most reliably useful tools in all of quant finance.

The intuition

GARCH (Generalised AutoRegressive Conditional Heteroskedasticity — the name is worse than the idea) says today's variance depends on:

• Recent squared returns — yesterday's shock raises today's expected volatility.
• Recent variance — volatility is persistent; a turbulent regime tends to continue.

In words: after a violent day, expect more violence tomorrow; after calm, expect calm. The model formalises the clustering everyone observes on a chart.

Why it matters more than return forecasting

You may not be able to forecast direction, but if you can forecast the size of moves you can:

• Size positions correctly — trade smaller when volatility is high, larger when it is low, targeting constant risk.
• Price options — volatility is the central input to option value.
• Set risk limits that adapt instead of using a stale fixed number.

Volatility-targeting strategies built on GARCH-style forecasts are a staple of professional risk management precisely because the thing being forecast (volatility) genuinely has memory, whereas returns barely do.

Honest limits

GARCH still assumes a particular structure and can be slow to react to a sudden regime change. It will not see a shock coming — it reacts after the first big move. But reacting fast and intelligently to changing volatility is itself a durable edge.