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Forecasting Equity Volatility with Implied Volatility and GARCH

Article Quant Q&A · Author: Winnie
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Summary

The document contrasts forward-looking and backward-looking approaches to estimating equity volatility. For a forecast horizon aligned with an options maturity, at-the-money-forward implied volatility can serve as a market-based estimate. Because implied volatility may include a premium over subsequently realized volatility, the response suggests estimating that premium from historical data or applying a rough adjustment. The VIX is described as an implied measure of expected S&P 500 volatility, while VIX futures reflect what the market may expect volatility to be at a future date.

For forecasts based on past returns, the discussion points to GARCH models, especially GJR-GARCH and EGARCH, which can represent the tendency for negative equity shocks to affect volatility more than positive shocks. It cites a study comparing implied-volatility methods with other models, but provides no detailed performance results. The material stresses that volatility is difficult to forecast and that estimates can be seriously wrong, potentially creating misplaced confidence in risk management. These approaches are starting points rather than reliable guarantees.

Key ideas

  • Match an option’s maturity to the volatility forecast horizon when using implied volatility.
  • Implied volatility may exceed realized volatility because of a premium that can be estimated from historical data.
  • VIX futures reflect expectations about future implied volatility, while the VIX measures S&P 500 implied volatility.
  • GJR-GARCH and EGARCH can account for asymmetric equity volatility responses to positive and negative shocks.
  • Treat volatility forecasts as uncertain indications because errors can undermine risk assessment.

Tags

EquitiesVolatilityOptionsFuturesRisk management
Full text
# How would you forecast volatility without using any programming languages or machine learning or anything of that sort?


# How would you forecast volatility without using any programming languages or machine learning or anything of that sort?












I am trying to forecast volatility. I am on the tactical asset allocation team. No one on our team knows machine learning or any programming languages. We are fundamental equity research analysts trying to find a way to forecast volatility. We were thinking of maybe using the VIX futures?

## Answer by RWP - Down by the Bay (score 3, accepted)

https://quant.stackexchange.com/a/53149

For asset allocation purposes I would use implied volatility on atmf options on the underlying with a maturity close to the term in which you are interested. There will be some premium in there so you can run a regression and find out how much premium on average is in there historically, or you can just divide by 1.1, which is a good approximation for the premium.

Example: Say 1mo S&P atmf options trade with implied volatility of 50, then your estimate for 1mo vol is 50/1.1 = 45.5

## Answer by Alba (score 6)

https://quant.stackexchange.com/a/53134

Basically, you have to choose whether to use a forward-looking or a backward-looking method of forecasting volatility. Let's start with the VIX. The VIX is an implied volatility index. Option pricing models require the volatility of the underlying asset as an input. Volatility is not an observed quantity, so the people who are pricing the options have to estimate it. This means that you can plug the market price of the option back into the pricing formula, and solve it backwards for the volatility, which will then roughly correspond to the market's estimate of what the volatility will be during the maturity period of the option. The VIX is an index that tracks this implied volatility, the underlying being the S&P 500 index. It used to be calculated on the S&P 100 index using index options, but nowadays the CBOE has switched the methodology to using the broader S&P 500 and a "variance swap"-based calculation. The interpretation is however basically the same, it measures how large the volatility is expected to be over the next 12 months. This is a forward-looking volatility measure: It incorporates information of what the market believes that the volatility will be in the future. See this whitepaper for more details.

VIX futures are futures on implied volatility. This means that their payoff is based on what the market, at some time in the future, will believe that the volatility will be during some maturity period. I am not sure why you would use futures on the VIX rather than just using the VIX itself.

The alternative is a backward-looking measure, i.e. forecasting volatility tomorrow based on what it has been during some period in the (recent) past. Then, a good place to start would be GARCH models (Generalized Autoregressive Conditional Heteroskedasticity). This is a (very) broad class of models, but I'd say that for equity, you might want to look into the GJR-GARCH model of Glosten, Jagannathan and Runkle (1993) or the E-GARCH model of Nelson (1991). The volatility of equity tends to be asymmetric, i.e. negative shocks might affect volatility more harshly as compared to positive shocks. The GJR- and EGARCH models take this into account.

Becker et. al (2007) compare implied volatility-based models to the performance of other types of volatility models. Many of these are very involved. I want to emphasize that forecasting volatility is a difficult endeavour, and from a risk-management perspective, there are arguments in favour of the view that one should not even attempt it. It can give you a false sense of security. Any volatility forecast should not be interpreted as certain, but rather as an indication that is prone to being terribly wrong.

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.