Conditional implied volatility

With the VIX level just crossing above 20 (percent) for the first time in 2013, it is worth exploring the conditional distribution of the near-term future value of this index, based on its current value.  The autocorrelation between these two measures (e.g., correlation of next month's VIX with this month's VIX) is 0.8, though we see that this tells only a small fraction of the story.

More distribution and Bayesian analysis forthcoming, but for now here are two related charts.  They both show the one-month ahead VIX distribution (horizontal x-axis), dependent on the current month’s VIX value (vertical y-axis).  With enough exposure to these charts, one can get a sense of the conditional distribution of the implied volatility measure.

The results show that this volatility measure is likely to stay in the upper teens through the end of June.

Box plot, with median:

Distribution dot plot:

Note that if the VIX was normally distributed, which it is not, we can learn more about the relation of serial correlation to expectations of one's dependent variable (e.g., future volatility).  See this article for more information: Behind conditional bivariate probabilities.