Apr 28

Forecasting volatility - Reader question

by David Harper, CFA, FRM, CIPM

FRM | Quant | |

Question from Jason:

I was wondering if you covered option volatility forecasting within the GARCH framework? If not, could you offer any ideas, using methodologies on your site to accomplish this task? - Jason

Hi Jason. I assume you refer to using GARCH(1,1) to forecast volatility forward several periods. (rather that estimating current volatility, sometimes the literature refers to a current estimate as a 'forecast').

This used to be a AIM in the FRM, but the formula itself dropped out of the curriculum this year. The t-period forward forecast derives directly from the GARCH(1,1) formula; using John Hull's notation (Chapter 19), the expected variance (square of volatility) forward (t) periods is given by:

garchforecast

It's an instructive formula: the term on the right is the product of the GARCH's series' compounded persistence (all of the weight not assigned to the long-run variance) and the current gap between variance and it's long-run average. If you imagine it's 1.0, the predicted series is flat forever at the current variance ("perfectly persistent"). Less than 1.0, and the predicted variance is "fading" to its long run average.

There is a whole body of work on this. Briefly, the other elegant approach to long-run forecasting is to use implied volatility. That is, the forecasted volatility is the volatility given by "inverting" the pricing model. The series of future option prices (theory says best are at-the-money) inverts to give you a series of forecasted volatilities. This is elegant but gravely infected with model risk: it's only correct if the model is correct.

Here is a previous screencast that I did exactly on this topic.

Here is an EditGrid example of using the GARCH() forecast:

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