Order Flow, Transaction Clock, and Normality of Asset Returns

  • Author(s): Thierry Ané, Hélyette Geman
  • Published: Dec 17, 2002
  • Pages: 2259-2284
  • DOI: 10.1111/0022-1082.00286

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.

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