May 03

Forecasting volatility with GARCH

by David Harper, CFA, FRM, CIPM

For FRM candidates, after you master GARCH(1,1), you should see that John Hull rearranges GARCH to solve for a future expected volatility. Given the following assumptions:

Long-run variance (V_L): the level to which variance is mean-reverting
alpha = weight assigned to the lagged, squared return
beta = weight assigned to the lagged variance
sigma_n = current variance
t = number of forward periods

Then the expected future variance (forward t periods) is given by:

It is probably easier to remember this way:

This says, the expected difference between the forward volatility and the long-run variance is given by: the product of (alpha+beta raised to the t power) and the current difference.

Here is an editgrid spreadsheet that performs the calculation. You can open your own read/write copy here, you can better understand this by interacting with the model (note: yellow color indicates an input, gray an output; e.g., if you input alpha and beta, then gamma is solved because these three must sum to one).