  We study distributions of realized variance (squared realized volatility) and
squared implied volatility, as represented by VIX and VXO indices. We find that
Generalized Beta distribution provide the best fits. These fits are much more
accurate for realized variance than for squared VIX and VXO -- possibly another
indicator that the latter have deficiencies in predicting the former. We also
show that there are noticeable differences between the distributions of the
1970-2017 realized variance and its 1990-2017 portion, for which VIX and VXO
became available. This may be indicative of a feedback effect that implied
volatility has on realized volatility. We also discuss the distribution of the
difference between squared implied volatility and realized variance and show
that, at the basic level, it is consistent with Pearson's correlations obtained
from linear regression.
