GARCH models vs VIX

I am examining how investor sentiment affects the probability of stock market crises. I am using methodology similar to this paper https://ideas.repec.org/p/dij/wpfarg/1110304.html.

VIX (equivalents) data for a Canada, China and Australia is either not available or only available from 2008 (I need data for 2001-2015). However, V-Lab provides predictions for various GARCH models for the stock indexes that I am interested in, for example: http://vlab.stern.nyu.edu/analysis/VOL.AS51%3AIND-R.GARCH

I haven't studied GARCH models and have only a basic understanding of their uses. My question is, can historical GARCH predictions be used as a measure of stock price volatility (instead of VIX)? And are they used for academic research in this way?

If not, what other measures are commonly used to proxy the volatility of a stock Index?

Thanks.

• You have stochastic volatility models too Jun 28, 2016 at 15:45

2 Answers

These are 2 completely different ways of estimating volatility.

GARCH models are calibrated on historical time series i.e. information provided under the real-world measure $\mathbb{P}$. Although you can obviously use them for forecasting, the core information which is used to build the model is backward-looking in nature (historical behaviour of the stock).

The VIX method on the other hand relies on live listed option prices i.e. information provided under the risk-neutral measure $\mathbb{Q}$. As such, the core information which is used to derive a volatility estimate is forward-looking in nature (equilibrum price seen by market participants).

Naively mixing both approaches would lead to comparing apples with oranges IMHO. Choosing one over the other really depends on what exactly you are trying to achieve.

If you have options data with long enough history you could always construct a comparable index by computing the implied volatilities and using a similar weighting methodology to VIX or looking at the implied volatility of the 1 month call/put with strike closest to the price at the observation date (i.e. one closest to 100% moneyness).

If you want an easier solution, you could always use indices for which a volatility index comparable to VIX are available. DAX and Eurostoxx are few that come to mind with data available from 2001 onwards.