Using GARCH to Model Implied Volatility

Summary

The note clarifies what a GARCH model estimates when implied volatility (IV), or its growth rate, is used as the dependent variable. A typical GARCH setup has a conditional-mean equation for that variable and a conditional-variance equation for the mean equation’s error. With returns in the mean equation, the variance equation models conditional return volatility. With IV as the dependent variable, it instead models changing uncertainty in IV—the volatility of volatility.

The answer frames this as a question of what quantity the researcher wants to study, rather than whether IV is forward-looking while GARCH is historical. The document does not assess a fitted model, provide empirical evidence, or discuss data transformations, distributions, or forecasting performance. It therefore offers a conceptual distinction, not guidance on whether a particular IV series is suitable or how to specify a complete model.

Key ideas

• A GARCH model typically pairs a conditional-mean equation with a conditional-variance equation for its errors.
• Using returns as the dependent variable lets the variance equation describe conditional return volatility.
• Using implied volatility or its growth rate as the dependent variable targets volatility in that series.
• The modeling choice depends on whether volatility of implied volatility is the quantity of interest.

Tags

# Can we model Implied volatility using GARCH?


# Can we model Implied volatility using GARCH?












Can I use Implied volatility as a dependent variable in a GARCH model? I believe my IV data shows ARCH effects and hence can I use it to model volatility of the volatility? I know literature has used logged price differences in GARCH model, So I am a little confused If IV can be used or not (Since GARCH models historical volatility whereas IV is a forward looking measure)?

## Answer by Stéphane (score 3, accepted)

https://quant.stackexchange.com/a/59169

I am not sure where you're going, but GARCH models usually have two equations: (1) an equation describing the conditional expectation of the dependent variable and (2) an equation describing the conditional variance of the error term in equation (1) as a process that is perfectly anticipated 1 period ahead.

When you use returns in equation (1), equation (2) is then used to filter out the condition volatility process from returns. If you say you want to model IV or its growth rate using GARCH, you're trying to model the volatility of IV.

Is this what you want to do?

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