Time transformations, intraday data, and volatility models

ABSTRACT In this paper, the author focuses on trade and quote data for IBM stock traded on the New York Stock Exchange. Two different frameworks for analyzing this dataset are presented. First, using regularly sampled observations, the intraday volatility of the midpoint of the bid-ask quotes is characterized by estimating GARCH and EGARCH models, with intraday seasonality being accounted for. The impact of trade process characteristics (traded volume, number of trades, and average volume per trade) on the volatility specifications are also highlighted. Second, irregularly spaced data are dealt with directly. Two time transformations are reviewed that allow a thinning of the original dataset such that new durations are defined. The newly defined price and volume durations are characterized and the performance of the Log-ACD model for modeling these durations is assessed. Moreover, it is shown that price durations allow an easy computation of intraday volatility and that this method compares favorably with ARCH estimations. An application to intraday value-at-risk is presented in which both types of models are used to forecast the one-step-ahead value-at-risk.