1. Historical Behavior of VVIX June 2006 - February 2012
Chart 1a. The VIX® and VVIX, Time Series
Chart 1b. The VVIX versus the VIX® Sorted in Ascending Order
Chart 1a. is a graph of the time series of the VVIX and VIX® between June 2006 and February 2012; Chart 1b. shows the variation of the VVIX when the VIX® is sorted in ascending order. Several features are apparent from these charts and from an analysis of index returns:
The range of values of the VVIX is at a significantly higher level than that of the VIX®.
The VVIX ranges between 60 and 145 around an average of 86. The VIX ranges between 10 and 81 around an average of 24. Also note that the range of variation of the VVIX tends to widen at higher values of the VIX.
Except at high values of VIX, there is little correlation between variations of the VIX® and VVIX.
The VVIX and VIX® both reached local peaks in October 2008, during the credit crisis of 2008 and in May 2010, the "flash crash" month. In general however, the relationship between their variations is weaker than the relationship between the VIX® and the S&P 500.
Since the flash crash of May 2010, the VVIX has rarely dropped below 80.
This suggests that a new volatility regime came about after the flash crash. Market participants appear to have become more tentative about the future value of the VIX®.
The following additional features of VVIX characterize its term structure and its tendency to mean revert.
The VVIX tends to revert to its historical mean.
Since the VVIX is a rate variable, it is mean reverting. Table 1 shows the historical value of the VVIX 30, 60 and 90 days later, starting from different initial intervals. For example, when the initial value of the VVIX is between 30 and 50, its average value 30 days later is 78. The mean reversion is centered about the historical mean of VVIX, approximately 85 and the fixed point is the interval from 80 to 90 volatility points. Starting from this interval, the VVIX ends in the same interval. Starting from an initial value below its historical mean, the VVIX tends to end in a higher range in subsequent months. Conversely, from an initial value above its historical mean, the VVIX tends to revert to a lower range.
Table 1 Mean Reversion of VVIX
The term structure of the VVIX is downward sloping
Based on past history, the term structure of the VVIX is downward sloping. This is normal because a forward price is a forecast, and a short term forecast tends to be more volatile than a long-term forecast.
Chart 2 Term Structure of the VVIX