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    Asset prices are Brownian Motion: only in business time

    Geman, Helyette and Madan, D.B. and Yor, M. (2000) Asset prices are Brownian Motion: only in business time. In: Avellaneda, M. (ed.) Quantitative Analysis in Financial Markets. World Scientific Publishing Company. ISBN 9789810242268.

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    Abstract

    This paper argues that asset price processes arising from market clearing conditions should be modeled as pure jump processes, with no continuous martingale component. However, we show that continuity and normality can always be obtained after a time change. We study various examples of time changes and show that in all cases they are related to measures of economic activity. For the most general class of processes, the time change is a size-weighted sum of order arrivals. The paper provides a number of new processes for modeling prices. Characteristic functions for these processes are also given in closed form.

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