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Relative volume as a doubly stochastic binomial point process


  • James McCulloch


Relative intra-day cumulative volume is intra-day cumulative volume divided by final total volume. If intra-day cumulative volume is modeled as a Cox (doubly stochastic Poisson) point process, then using initial enlargement of filtration with the filtration of the Cox process enlarged by knowledge of final volume, it is shown that relative intra-day volume conditionally has a binomial distribution and is a novel generalization of a binomial point process: the doubly stochastic binomial point process. Re-scaling the intra-day traded volume to a relative volume between 0 (no volume traded) and 1 (daily trading completed) allows empirical intra-day volume distribution information for all stocks to be used collectively to estimate and identify the random intensity component of the doubly stochastic binomial point process and closely related Cox point process.

Suggested Citation

  • James McCulloch, 2007. "Relative volume as a doubly stochastic binomial point process," Quantitative Finance, Taylor & Francis Journals, vol. 7(1), pages 55-62.
  • Handle: RePEc:taf:quantf:v:7:y:2007:i:1:p:55-62 DOI: 10.1080/14697680600969735

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    References listed on IDEAS

    1. Tina Hviid Rydberg & Neil Shephard, 2000. "BIN Models for Trade-by-Trade Data. Modelling the Number of Trades in a Fixed Interval of Time," Econometric Society World Congress 2000 Contributed Papers 0740, Econometric Society.
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    Cited by:

    1. Olivier Gu'eant & Guillaume Royer, 2013. "VWAP execution and guaranteed VWAP," Papers 1306.2832,, revised May 2014.
    2. Bialkowski, Jedrzej & Darolles, Serge & Le Fol, Gaëlle, 2008. "Improving VWAP strategies: A dynamic volume approach," Journal of Banking & Finance, Elsevier, vol. 32(9), pages 1709-1722, September.
    3. McCulloch, James, 2012. "Fractal market time," Journal of Empirical Finance, Elsevier, vol. 19(5), pages 686-701.
    4. James McCulloch, 2012. "Fractal Market Time," Research Paper Series 311, Quantitative Finance Research Centre, University of Technology, Sydney.
    5. Jedrzej Bialkowski & Serge Darolles & Gaëlle Le Fol, 2005. "Decomposing Volume for VWAP Strategies," Working Papers 2005-16, Center for Research in Economics and Statistics.
    6. James McCulloch & Vladimir Kazakov, 2007. "Optimal VWAP Trading Strategy and Relative Volume," Research Paper Series 201, Quantitative Finance Research Centre, University of Technology, Sydney.
    7. Dieter Hendricks & Diane Wilcox, 2014. "A reinforcement learning extension to the Almgren-Chriss model for optimal trade execution," Papers 1403.2229,


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