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Asset Prices Are Brownian Motion: Only In Business Time

In: Quantitative Analysis In Financial Markets Collected Papers of the New York University Mathematical Finance Seminar(Volume II)

Author

Listed:
  • 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)

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.

Suggested Citation

  • Helyette Geman & Dilip B. Madan & Marc Yor, 2001. "Asset Prices Are Brownian Motion: Only In Business Time," World Scientific Book Chapters, in: Marco Avellaneda (ed.), Quantitative Analysis In Financial Markets Collected Papers of the New York University Mathematical Finance Seminar(Volume II), chapter 4, pages 103-146, World Scientific Publishing Co. Pte. Ltd..
    • Handle: RePEc:wsi:wschap:9789812810663_0004
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    Citations

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    Cited by:

    1. Figueiredo, Annibal & Gleria, Iram & Matsushita, Raul & Da Silva, Sergio, 2006. "The Levy sections theorem revisited," MPRA Paper 1983, University Library of Munich, Germany.
    2. Eckhard Platen & Renata Rendek, 2009. "Exact Scenario Simulation for Selected Multi-dimensional Stochastic Processes," Research Paper Series 259, Quantitative Finance Research Centre, University of Technology, Sydney.
    3. Kevin Fergusson & Eckhard Platen, 2006. "On the Distributional Characterization of Daily Log-Returns of a World Stock Index," Applied Mathematical Finance, Taylor & Francis Journals, vol. 13(1), pages 19-38.
    4. Mauricio Junca & Rafael Serrano, 2014. "Utility maximization in pure-jump models driven by marked point processes and nonlinear wealth dynamics," Papers 1411.1103, arXiv.org, revised Sep 2015.
    5. Ciuiu Daniel, 2014. "The Jackson Queueing Network Model Built Using Poisson Measures. Application To A Bank Model," Folia Oeconomica Stetinensia, Sciendo, vol. 13(2), pages 7-22, July.
    6. Teneng, Dean, 2013. "Outperforming the naïve Random Walk forecast of foreign exchange daily closing prices using Variance Gamma and normal inverse Gaussian Levy processes," MPRA Paper 47851, University Library of Munich, Germany.
    7. Tianyao Chen & Xue Cheng & Jingping Yang, 2019. "Common Decomposition of Correlated Brownian Motions and its Financial Applications," Papers 1907.03295, arXiv.org, revised Nov 2020.
    8. Renata Rendek, 2013. "Modeling Diversified Equity Indices," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 23, July-Dece.
    9. Evis Këllezi & Nick Webber, 2004. "Valuing Bermudan options when asset returns are Levy processes," Quantitative Finance, Taylor & Francis Journals, vol. 4(1), pages 87-100.
    10. Renata Rendek, 2013. "Modeling Diversified Equity Indices," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 4-2013, January-A.
    11. Ciuiu, Daniel, 2011. "Homogeneity tests for Levy processes and applications," MPRA Paper 36457, University Library of Munich, Germany, revised Nov 2011.

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