Information Arrival as a Stochastic Clock for Intraday Trading

Abstract

Financial markets do not evolve uniformly through calendar time. Periods of intense information arrival accelerate market activity, while information-poor periods produce the familiar intraday lull in trading. We propose a stochastic clock framework in which business time is generated by the information arrival process, providing a unified explanation for intraday trading intensity, volume, realized volatility, and execution risk. To formalize this idea, we develop a compound Hawkes model consisting of a deterministic bathtub-shaped baseline intensity, a marked linear trade-feedback component, and a squared-mark news channel that treats equal-magnitude positive and negative information symmetrically at the event level. The same signed news mark enters expected price changes linearly but enters trading intensity quadratically. The model therefore predicts opposite expected price responses but identical activity and conditional residual-variance responses to equal-magnitude positive and negative news. Under a clock law of large numbers and finite-moment conditions, the trade-time component of midpoint log price admits a diffusive limit with variance proportional to average trading intensity. The model also yields a closed-form parametric VWAP profile and a set of directly testable predictions linking information flow to trading activity and volatility. The framework provides a parsimonious theoretical foundation for understanding how information arrival governs the speed of financial markets.