Price and Volatility Using High-Frequency Data

It is often assumed that the price time series have a well-defined continuum limit and that high-frequency data bring us closer to this limit. But because of the discrete trading process, a new incoherent term need to be added to the hypothetical continuum prices. This term limits severely the amount of information that can be extracted from high-frequency time series. This chapter presents various ways to remove the incoherent term in order to obtain estimators based only on the continuous price, consistent with estimators at lower frequencies. This is essential for the volatility, which otherwise is strongly biased upward when using the naive estimators. Various high-frequency volatility estimators are presented, based either on multiple time scales or on lagged covariances. Estimators for the hypothetical underlying prices are also discussed, as well as estimators of the volatility per tick.