Apr 26

Long run variance in GARCH(1,1)

by David Harper, CFA, FRM, CIPM

Omega2

Previously we saw that GARCH(1,1) estimates volatility as a function of three terms:

Garch_400w

In English, the volatility estimate reverts toward its long-run average (the first term) as a function of yesterday's squared return (second term) and yesterday's variance (third term). The greeks are the weights assigned to each factor; they sum to one.

John Hull also writes the first term with omega:

Garch_womega

The first term is a constant, but it's not the long-run average variance (new learners make this mistake): the first term is the weight multiplied by the long-run variance.

Here is a working spreadsheet example:

EditGrid Spreadsheet by user/davidharper.

Try this for mastery: can you solve for the long-run average variance as a function of the other parameters?

Here's how: