The Telescoping Overlap Problem in Options Data

In analyzing the relation between implied and realized volatility, researchers confront samples that have a high degree of overlap, which quot;telescopesquot; as option maturities are reached. With volatility samples of this nature, we show that the regression coefficients are disperse even in the limit, the t-statistics diverge, the Durbin-Watson statistic converges to zero, and the regression R2 converges to a positive random variable in the limit. We develop an alternative asymptotic theory that accounts for both the high degree of overlap and its telescoping nature, and illustrate it empirically with an application to Samp;P 100 (OEX) index options. Our theory reconciles the seemingly contradictory results from overlapping and non-overlapping samples, and suggests that option markets aggregate volatility information efficiently, as suggested by the (statistically consistent) results from non-overlapping samples