Distribution of Historic Market Data – Implied and Realized Volatility

Abstract

We undertake a systematic comparison between implied volatility, as represented by VIX (new methodology) and VXO (old methodology) and realized volatility. We do not find substantial difference in accuracy between VIX and VXO. We compare visually and statistically the distributions of realized and implied variance (volatility squared) and study the distribution of their ratio. The ratio distributions are studied both for the known realized variance (for the current month) and for the predicted realized variance (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.