GARCH Forecasts and Implied Volatility as Different Measures
Summary
The document compares volatility estimates from GARCH models with estimates derived from option prices, in the context of studying stock-market crisis probability and investor sentiment. GARCH models use historical index behavior to estimate or forecast volatility under the real-world probability measure. A VIX-style measure is inferred from listed options and reflects prices under the risk-neutral measure, so it represents market-implied expectations rather than the same quantity as a historical-data model.
The response cautions that the two approaches should not be treated as interchangeable; the suitable choice depends on the research question. As alternatives when a local volatility index is unavailable, it suggests constructing a comparable implied-volatility measure from options data or using an index with a longer history of an established volatility benchmark. These are options rather than a definitive recommendation, and the document does not evaluate their empirical performance or address the limitations of particular GARCH specifications.
Key ideas
- GARCH estimates use historical time-series information and can be used to forecast volatility.
- VIX-style measures derive from option prices and represent risk-neutral implied volatility.
- The two measures answer different questions and should not be compared as if equivalent.
- A researcher can construct an implied-volatility measure from options or select an index with a longer benchmark history.
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Full text
# GARCH models vs VIX
# 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.
## Answer by Quantuple (score 8, accepted)
https://quant.stackexchange.com/a/27839
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.
## Answer by Ana (score 2)
https://quant.stackexchange.com/a/27859
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.Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.