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Relative Volume as a Doubly Stochastic Binomial Point Process

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  • James McCulloch

Abstract

If intra-day volume is modelled as a Cox point process, then relative intra-day cumulative volume (intra-day cumulative volume divided by final total volume) is shown to be 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 binomial point process and closely related Cox point process. This is useful for Volume Weighted Average Price (VWAP) traders who require a stochastic model of relative intra-day cumulative volume to implement risk-optimal VWAP trading strategies.

Suggested Citation

  • James McCulloch, 2005. "Relative Volume as a Doubly Stochastic Binomial Point Process," Research Paper Series 146, Quantitative Finance Research Centre, University of Technology, Sydney.
  • Handle: RePEc:uts:rpaper:146
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    File URL: http://www.qfrc.uts.edu.au/research/research_papers/rp146.pdf
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    References listed on IDEAS

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    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, arXiv.org, 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, arXiv.org.

    More about this item

    Keywords

    binomial; point process; doubly stochastic; relative volume; Cox process; random probability measure; VWAP; volume weighted average pricing; NYSE; New York Stock Exchange;

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