VIX vs GARCH: Results from a New Region of Phase Space

In the article Our New Volatility Laboratory, we discussed the impact of exploring a new region of volatility phase space on our econometric modelling procedures. That discussion exhibited the Dow Jones Industrial Average, which is an index I regularly trade futures on. However, the recent dramatic increases in the level of volatility have not been restricted just to the DOW.

The chart SPX Volatility compactly illustrates the volatility of the S&P 500 index since 1995. The volatility model presented here is a simple GARCH model that was developed on the 2000-2003 daily data and is quoted in terms of daily volatility in index points.

In the chart Comparison of VIX with Volatility Model we compare the VIX index, published by the CBOE and designed to represent the annualized volatility of the S&P 500 index, over the next 30 days, implied by the current market in index options, with the GARCH model discussed above.

We see very strong agreement between the VIX and the GARCH model with a regression line gradient statistically indistinct from unity. This indicates that changes in the VIX and changes in the GARCH model track eachother quite well. However, there does seem to be a persistent and significant premium in the VIX over the GARCH model of about 4%. (In the scatter plot the blue line is the regression line and the green line is a line with unit gradient and zero intercept.)

However, if we examine the tail of the scatter, which is the data where volatility is significantly higher than the norm, we see that this relationship is not true. All this data lies below the regression line. Thus, if we assumed that now would be a good time to sell volatility we might be making a mistake as rather than being very expensive, volatility may be a little cheap right now.