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Preferred numbers and the distributions of trade sizes and trading volumes in the Chinese stock market

Author

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  • G.-H. Mu
  • W. Chen
  • J. Kertész
  • W.-X. Zhou

Abstract

The distribution of trade sizes and trading volumes are investigated based on the limit order book data of 22 liquid Chinese stocks listed on the Shenzhen Stock Exchange in the whole year 2003. We observe that the size distribution of trades for individual stocks exhibits jumps, which is caused by the number preference of traders when placing orders. We analyze the applicability of the "$q$-Gamma" function for fitting the distribution by the Cram\'{e}r-von Mises criterion. The empirical PDFs of trading volumes at different timescales $\Delta{t}$ ranging from 1 min to 240 min can be well modeled. The applicability of the $q$-Gamma functions for multiple trades is restricted to the transaction numbers $\Delta{n}\leqslant8$. We find that all the PDFs have power-law tails for large volumes. Using careful estimation of the average tail exponents $\alpha$ of the distribution of trade sizes and trading volumes, we get $\alpha>2$, well outside the L{\'e}vy regime.
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Suggested Citation

  • G.-H. Mu & W. Chen & J. Kertész & W.-X. Zhou, 2009. "Preferred numbers and the distributions of trade sizes and trading volumes in the Chinese stock market," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 68(1), pages 145-152, March.
    • Handle: RePEc:spr:eurphb:v:68:y:2009:i:1:p:145-152
    DOI: 10.1140/epjb/e2009-00059-9
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    Cited by:

    1. Lautier, Delphine & Raynaud, Franck, 2011. "Statistical properties of derivatives: A journey in term structures," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(11), pages 2009-2019.
    2. Wei-Xing Zhou, 2012. "Universal price impact functions of individual trades in an order-driven market," Quantitative Finance, Taylor & Francis Journals, vol. 12(8), pages 1253-1263, June.
    3. Li, Ming-Xia & Jiang, Zhi-Qiang & Xie, Wen-Jie & Xiong, Xiong & Zhang, Wei & Zhou, Wei-Xing, 2015. "Unveiling correlations between financial variables and topological metrics of trading networks: Evidence from a stock and its warrant," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 419(C), pages 575-584.
    4. Lallouache, Mehdi & Abergel, Frédéric, 2014. "Tick size reduction and price clustering in a FX order book," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 416(C), pages 488-498.
    5. Pankaj Kumar, 2021. "Deep Hawkes Process for High-Frequency Market Making," Papers 2109.15110, arXiv.org.
    6. Michelle B Graczyk & Sílvio M Duarte Queirós, 2017. "Intraday seasonalities and nonstationarity of trading volume in financial markets: Collective features," PLOS ONE, Public Library of Science, vol. 12(7), pages 1-23, July.
    7. Matthias Schnaubelt & Jonas Rende & Christopher Krauss, 2019. "Testing Stylized Facts of Bitcoin Limit Order Books," JRFM, MDPI, vol. 12(1), pages 1-30, February.
    8. Jiang, Zhi-Qiang & Zhou, Wei-Xing, 2010. "Complex stock trading network among investors," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(21), pages 4929-4941.
    9. Bai, Man-Ying & Zhu, Hai-Bo, 2010. "Power law and multiscaling properties of the Chinese stock market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(9), pages 1883-1890.
    10. Martin D. Gould & Mason A. Porter & Sam D. Howison, 2015. "Quasi-Centralized Limit Order Books," Papers 1502.00680, arXiv.org, revised Oct 2016.
    11. Gao-Feng Gu & Xiong Xiong & Hai-Chuan Xu & Wei Zhang & Yongjie Zhang & Wei Chen & Wei-Xing Zhou, 2021. "An empirical behavioral order-driven model with price limit rules," Financial Innovation, Springer;Southwestern University of Finance and Economics, vol. 7(1), pages 1-24, December.
    12. Zhang, Ting & Gu, Gao-Feng & Xu, Hai-Chuan & Xiong, Xiong & Chen, Wei & Zhou, Wei-Xing, 2017. "Power-law tails in the distribution of order imbalance," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 483(C), pages 201-208.
    13. Sun, Xiao-Qian & Cheng, Xue-Qi & Shen, Hua-Wei & Wang, Zhao-Yang, 2011. "Distinguishing manipulated stocks via trading network analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(20), pages 3427-3434.
    14. Ni, Xiao-Hui & Jiang, Zhi-Qiang & Gu, Gao-Feng & Ren, Fei & Chen, Wei & Zhou, Wei-Xing, 2010. "Scaling and memory in the non-Poisson process of limit order cancelation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(14), pages 2751-2761.
    15. Wu, Ting & Wang, Yue & Li, Ming-Xia, 2017. "Post-hit dynamics of price limit hits in the Chinese stock markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 465(C), pages 464-471.
    16. Zhang, Ting & Gu, Gao-Feng & Zhou, Wei-Xing, 2019. "Order imbalances and market efficiency: New evidence from the Chinese stock market," Emerging Markets Review, Elsevier, vol. 38(C), pages 458-467.
    17. Li, Mu-Yao & Cai, Qing & Gu, Gao-Feng & Zhou, Wei-Xing, 2019. "Exponentially decayed double power-law distribution of Bitcoin trade sizes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 535(C).
    18. Martin D. Gould & Mason A. Porter & Stacy Williams & Mark McDonald & Daniel J. Fenn & Sam D. Howison, 2013. "Limit order books," Quantitative Finance, Taylor & Francis Journals, vol. 13(11), pages 1709-1742, November.
    19. Martin D. Gould & Mason A. Porter & Stacy Williams & Mark McDonald & Daniel J. Fenn & Sam D. Howison, 2010. "Limit Order Books," Papers 1012.0349, arXiv.org, revised Apr 2013.
    20. Gu, Gao-Feng & Ren, Fei & Ni, Xiao-Hui & Chen, Wei & Zhou, Wei-Xing, 2010. "Empirical regularities of opening call auction in Chinese stock market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(2), pages 278-286.
    21. Luo, Jiawen & Chen, Langnan & Liu, Hao, 2013. "Distribution characteristics of stock market liquidity," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(23), pages 6004-6014.
    22. Xiao-Qian Sun & Xue-Qi Cheng & Hua-Wei Shen & Zhao-Yang Wang, 2011. "Distinguishing manipulated stocks via trading network analysis," Papers 1110.2260, arXiv.org.

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