ASSET PRICES ARE BROWNIAN MOTION: ONLY IN BUSINESS TIME

Helyette Geman, Dilip B. Madan and Marc Yor
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Helyette Geman: University Paris IX Dauphine and ESSEC, France
Dilip B. Madan: University of Maryland, USA
Marc Yor: University Paris VI - Laboratoire de Probabilités, France

Chapter 4 in Quantitative Analysis in Financial Markets:Collected Papers of the New York University Mathematical Finance Seminar(Volume II), 2001, pp 103-146 from World Scientific Publishing Co. Pte. Ltd.

Abstract: AbstractThis 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.

Date: 2001
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