Spurious long memory, uncommon breaks and the implied–realized volatility puzzle

Abstract

One of the puzzles in international finance is the frequent finding that implied volatility is a biased predictor of realized volatility. However, given asset price volatility is often characterized as possessing long memory, the recent literature has shown that allowing for long-range dependence removes this bias. Of course, the appearance of long memory can be generated by the presence of structural breaks. This paper discusses the effect of structural breaks on the implied–realized volatility relation. Simulations show that if significant structural breaks are omitted, testing can spuriously show the typical patterns of fractional cointegration found in the literature. Next, empirical results show that foreign exchange implied and realized volatility contains structural breaks. The breaks in the implied series never closely anticipate or co-occur with those of the realized series, suggesting that the market has no ability to forecast structural change. When breaks are accounted for in the bi-variate framework, the point estimate of the slope parameter falls and the null of unbiasedness can be rejected. Allowing for structural breaks suggests that the implied–realized volatility puzzle might not be solved after all.