Order Flow, Transaction Clock, and Normality of Asset Returns |
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Authors: | Thierry Ané & Hélyette Geman |
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Institution: | University Paris Dauphine,;ESSEC Graduate Business School and the University Paris Dauphine |
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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. |
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