A Distributional Approach to Realized Volatility

This paper proposes new measures of the integrated variance, measures which use high-frequency bid-ask spreads and quoted depths. The traditional approach assumes that the mid-quote is a good measure of frictionless price. However, the recent high-frequency econometric literature takes the mid-quote as a noisy measure of the frictionless price and proposes new and robust estimators of the integrated variance. This paper forgoes the common assumption of an additive friction term, and demonstrates how the quoted depth may be used in the construction of refined realized volatility measures under the assumption that the true frictionless price lies between the bid and the ask. More specifically, we make assumptions about the conditional distribution of the frictionless price given the available information, including quotes and depths. This distributional assumption leads to new measures of the integrated variance that explicitly incorporate the depths. We then empirically compare the new measures with the robust ones when dealing with forecasting integrated variance or trading options. We show that, in several cases, the new measures dominate the traditional measures.