Implied and Realized Volatility: A Study of the Ratio Distribution

TL;DR

This paper investigates the relationship between implied volatility indices and realized variances, revealing that their ratio follows a Beta Prime distribution with parameters depending on the specific month analyzed.

Contribution

It introduces a novel statistical model for the ratio of implied to realized volatility, showing the Beta Prime distribution fits well and varies with the month.

Findings

The ratio of implied to realized volatility fits a Beta Prime distribution.

Shape parameters of the distribution depend on the month analyzed.

The model improves understanding of volatility dynamics.

Abstract

We analyze correlations between squared volatility indices, VIX and VXO, and realized variances -- the known one, for the current month, and the predicted one, for the following month. We show that the ratio of the two is best fitted by a Beta Prime distribution, whose shape parameters depend strongly on which of the two months is used.