Forecasting Realized Variance with VIX, EWMA, and GARCH
Summary
The document describes a comparison of daily close-to-close equity-index variance forecasts using EWMA, GARCH, and squared VIX. The author evaluates predictions against squared S&P 500 returns with average absolute error, mean squared error, and regression, and also compares forecasts with longer-term averages to reduce the influence of noise in individual squared returns. In the reported experiments, EWMA and GARCH perform similarly, while squared VIX performs better.
The author recognizes that implied volatility can exceed subsequent realized volatility because of a volatility risk premium, and reports that subtracting rolling estimates of that premium worsened the forecasts. A response cautions that such adjustments depend on implementation and may degrade performance. Another response suggests deriving implied volatility from option prices and the underlying price using Black–Scholes. These are limited observations rather than a controlled comparison across markets or regimes; the document supplies no detailed sample design, parameter choices, or out-of-sample results.
Key ideas
- Squared returns are noisy targets, so the author also compares forecasts with longer-term realized variance averages.
- In the reported S&P 500 tests, EWMA and GARCH perform similarly, while squared VIX performs better.
- The author’s rolling volatility-risk-premium adjustment worsens the estimates.
- The response cautions that risk-premium estimates depend on implementation.
- Implied volatility can be inferred from option prices using a pricing model such as Black–Scholes.
Tags
Full text
# How to predict realised variance? # How to predict realised variance? I am trying to predict the realised daily close to close variance of an equity index. I checked the literature on volatility forecasting and tried a bunch of things on a dataset for the S&P 500. The most promising approached were an EWMA, GARCH and just using the squared VIX. I measured the performance of my predictions by looking at average absolute error, mean squared error and also doing a regression between my predictor and the actual squared returns. I am aware that squared returns are very noisy, so I also took longer term averages of them and checked how well my predictors forecasts these averages. EWMA and GARCH showed a similar performance. I was surprised to see that the VIX did much better. I can clearly see that VIX is biased, since there is the volatility risk premium. Implied vol is on average higher than realised vol, since option sellers want to be compensated, but of course there are exceptions. I tried to remove the volatility risk premium from the VIX by subtracting some rolling averages of the realised risk premium, hoping that this would remove the bias, but my estimation got much worse afterwards. Does anyone have some experience on this type of problem? Can you confirm my observations? Are there other methods I could try? ## Answer by RWP - Down by the Bay (score 1) https://quant.stackexchange.com/a/54334 EWMA and GARCH are good methods. If you can do better than using the VIX then you should not post online about it and instead just trade that yourself and make a ton of money! Seriously. I don't love the sound of subtracting some rolling averages of the realized risk premium. While I could see that working because the risk premium does change over time, it also relies heavily on your specific implementation and could result in something quite poor. Years ago when I looked at this I saw something like 1.07x for the ex-ante implied/ex-post realized premium over a decade plus. You can find that easily from your data. ## Answer by user28909 (score 0) https://quant.stackexchange.com/a/54369 You can use blackscholes, use option price and current price and solve for implied vol.
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.