Order Flow, Transaction Clock, and Normality of Asset Returns

Authors

  • Thierry Ané,

    Search for more papers by this author
    • Ané is from the University Paris Dauphine. Geman is from the University Paris Dauphine and ESSEC Graduate Business School. We thank the Center for International Securities and Derivative Markets of the University of Massachusetts for providing the data. We appreciate the comments made by participants of the Finance Seminar of the University of Chicago, the University of Washington, the University of Maryland, Carnegie Mellon University, the Workshop on “Stochastics, Information and Markets” at Humboldt University, and the European Finance Association meeting in Fontainebleau. The suggestions by René Stulz (the editor) and an anonymous referee were particularly helpful.
  • Hélyette Geman

    Search for more papers by this author
    • Ané is from the University Paris Dauphine. Geman is from the University Paris Dauphine and ESSEC Graduate Business School. We thank the Center for International Securities and Derivative Markets of the University of Massachusetts for providing the data. We appreciate the comments made by participants of the Finance Seminar of the University of Chicago, the University of Washington, the University of Maryland, Carnegie Mellon University, the Workshop on “Stochastics, Information and Markets” at Humboldt University, and the European Finance Association meeting in Fontainebleau. The suggestions by René Stulz (the editor) and an anonymous referee were particularly helpful.

Abstract

The goal of this paper is to show that normality of asset returns can be recovered through a stochastic time change. Clark (1973) addressed this issue by representing the price process as a subordinated process with volume as the lognormally distributed subordinator. We extend Clark's results and find the following: (i) stochastic time changes are mathematically much less constraining than subordinators; (ii) the cumulative number of trades is a better stochastic clock than the volume for generating virtually perfect normality in returns; (iii) this clock can be modeled nonparametrically, allowing both the time-change and price processes to take the form of jump diffusions.

Ancillary