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Empirical shape function of limit-order books in the Chinese stock market

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  • Gu, Gao-Feng
  • Chen, Wei
  • Zhou, Wei-Xing

Abstract

We have analyzed the statistical probabilities of limit-order book (LOB) shape through building the book using the ultra-high-frequency data from 23 liquid stocks traded on the Shenzhen Stock Exchange in 2003. We find that the averaged LOB shape has a maximum away from the same best price for both buy and sell sides of the LOB. The LOB shape function has nice exponential form in the right tail. The buy side of the LOB is found to be abnormally thicker for the price levels close to the same best although there are much more sell orders on the book. We also find that the LOB shape functions for both buy and sell sides have periodic peaks with a period of five. The 1-min averaged volumes at fixed tick level follow log-normal distributions except for the left tails which display power-law behaviors, exhibit abnormal intraday patterns with increasing trend, and possess long memory that cannot be explained by the intraday patterns. Academic implications of our empirical results are also briefly discussed.

Suggested Citation

  • Gu, Gao-Feng & Chen, Wei & Zhou, Wei-Xing, 2008. "Empirical shape function of limit-order books in the Chinese stock market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(21), pages 5182-5188.
    • Handle: RePEc:eee:phsmap:v:387:y:2008:i:21:p:5182-5188
    DOI: 10.1016/j.physa.2008.05.008
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    1. Gao-Feng Gu & Wei Chen & Wei-Xing Zhou, 2006. "Quantifying bid-ask spreads in the Chinese stock market using limit-order book data: Intraday pattern, probability distribution, long memory, and multifractal nature," Papers physics/0701017, arXiv.org, revised Mar 2007.
    2. Dorogovtsev, S.N. & Mendes, J.F.F. & Oliveira, J.G., 2006. "Frequency of occurrence of numbers in the World Wide Web," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 360(2), pages 548-556.
    3. Jean-Philippe Bouchaud & Yuval Gefen & Marc Potters & Matthieu Wyart, 2004. "Fluctuations and response in financial markets: the subtle nature of 'random' price changes," Quantitative Finance, Taylor & Francis Journals, vol. 4(2), pages 176-190.
    4. P. Weber & B. Rosenow, 2005. "Order book approach to price impact," Quantitative Finance, Taylor & Francis Journals, vol. 5(4), pages 357-364.
    5. Sergei Maslov & Mark Mills, 2001. "Price fluctuations from the order book perspective - empirical facts and a simple model," Papers cond-mat/0102518, arXiv.org.
    6. Maskawa, Jun-ichi, 2007. "Correlation of coming limit price with order book in stock markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 383(1), pages 90-95.
    7. Jean-Philippe Bouchaud & Marc Mezard & Marc Potters, 2002. "Statistical properties of stock order books: empirical results and models," Quantitative Finance, Taylor & Francis Journals, vol. 2(4), pages 251-256.
    8. Challet, Damien & Stinchcombe, Robin, 2001. "Analyzing and modeling 1+1d markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 300(1), pages 285-299.
    9. Lillo Fabrizio & Farmer J. Doyne, 2004. "The Long Memory of the Efficient Market," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 8(3), pages 1-35, September.
    10. Ranaldo, Angelo, 2004. "Order aggressiveness in limit order book markets," Journal of Financial Markets, Elsevier, vol. 7(1), pages 53-74, January.
    11. Parameswaran Gopikrishnan & Vasiliki Plerou & Xavier Gabaix & H. Eugene Stanley, 2000. "Statistical Properties of Share Volume Traded in Financial Markets," Papers cond-mat/0008113, arXiv.org.
    12. Zhou, Wei-Xing & Sornette, Didier, 2004. "Antibubble and prediction of China's stock market and real-estate," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 337(1), pages 243-268.
    13. Potters, Marc & Bouchaud, Jean-Philippe, 2003. "More statistical properties of order books and price impact," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 324(1), pages 133-140.
    14. Zoltan Eisler & Janos Kertesz & Fabrizio Lillo, 2007. "The limit order book on different time scales," Papers 0705.4023, arXiv.org.
    15. Mike, Szabolcs & Farmer, J. Doyne, 2008. "An empirical behavioral model of liquidity and volatility," Journal of Economic Dynamics and Control, Elsevier, vol. 32(1), pages 200-234, January.
    16. J. Doyne Farmer & Laszlo Gillemot & Fabrizio Lillo & Szabolcs Mike & Anindya Sen, 2004. "What really causes large price changes?," Quantitative Finance, Taylor & Francis Journals, vol. 4(4), pages 383-397.
    17. Gu, Gao-Feng & Chen, Wei & Zhou, Wei-Xing, 2008. "Empirical regularities of order placement in the Chinese stock market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(13), pages 3173-3182.
    18. Maslov, Sergei & Mills, Mark, 2001. "Price fluctuations from the order book perspective—empirical facts and a simple model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 299(1), pages 234-246.
    19. Philipp Weber & Bernd Rosenow, 2006. "Large stock price changes: volume or liquidity?," Quantitative Finance, Taylor & Francis Journals, vol. 6(1), pages 7-14.
    20. Gu, Gao-Feng & Chen, Wei & Zhou, Wei-Xing, 2008. "Empirical distributions of Chinese stock returns at different microscopic timescales," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(2), pages 495-502.
    21. Robert F. Engle, 2000. "The Econometrics of Ultra-High Frequency Data," Econometrica, Econometric Society, vol. 68(1), pages 1-22, January.
    22. Jean-Philippe Bouchaud & Marc Mezard & Marc Potters, 2002. "Statistical properties of stock order books: empirical results and models," Science & Finance (CFM) working paper archive 0203511, Science & Finance, Capital Fund Management.
    23. G.-F. Gu & W. Chen & W.-X. Zhou, 2007. "Quantifying bid-ask spreads in the Chinese stock market using limit-order book data," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 57(1), pages 81-87, May.
    24. Jun-ichi Maskawa, 2007. "Correlation of coming limit price with order book in stock markets," Papers physics/0702029, arXiv.org.
    25. Kantelhardt, Jan W & Koscielny-Bunde, Eva & Rego, Henio H.A & Havlin, Shlomo & Bunde, Armin, 2001. "Detecting long-range correlations with detrended fluctuation analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 295(3), pages 441-454.
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    6. Kylie-Anne Richards & Gareth W. Peters & William Dunsmuir, 2012. "Heavy-Tailed Features and Empirical Analysis of the Limit Order Book Volume Profiles in Futures Markets," Papers 1210.7215, arXiv.org, revised Apr 2015.
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    9. Yu-Lei Wan & Wen-Jie Xie & Gao-Feng Gu & Zhi-Qiang Jiang & Wei Chen & Xiong Xiong & Wei Zhang & Wei-Xing Zhou, 2015. "Statistical Properties and Pre-Hit Dynamics of Price Limit Hits in the Chinese Stock Markets," PLOS ONE, Public Library of Science, vol. 10(4), pages 1-20, April.
    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. Ioane Muni Toke, 2013. "The order book as a queueing system: average depth and influence of the size of limit orders," Papers 1311.5661, arXiv.org.
    12. Hai-Chuan Xu & Wei Chen & Xiong Xiong & Wei Zhang & Wei-Xing Zhou & H Eugene Stanley, 2016. "Limit-order book resiliency after effective market orders: Spread, depth and intensity," Papers 1602.00731, arXiv.org, revised Feb 2017.
    13. Ioane Muni Toke, 2015. "The order book as a queueing system: average depth and influence of the size of limit orders," Post-Print hal-01006410, HAL.
    14. 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.
    15. Gu, Gao-Feng & Xiong, Xiong & Zhang, Yong-Jie & Chen, Wei & Zhang, Wei & Zhou, Wei-Xing, 2016. "Stylized facts of price gaps in limit order books," Chaos, Solitons & Fractals, Elsevier, vol. 88(C), pages 48-58.
    16. Xuefeng Gao & S. J. Deng, 2014. "Hydrodynamic limit of order book dynamics," Papers 1411.7502, arXiv.org, revised Feb 2016.
    17. Gao-Feng Gu & Xiong Xiong & Yong-Jie Zhang & Wei Chen & Wei Zhang & Wei-Xing Zhou, 2014. "Stylized facts of price gaps in limit order books: Evidence from Chinese stocks," Papers 1405.1247, arXiv.org.
    18. Hugh L. Christensen & Richard E. Turner & Simon I. Hill & Simon J. Godsill, 2013. "Rebuilding the limit order book: sequential Bayesian inference on hidden states," Quantitative Finance, Taylor & Francis Journals, vol. 13(11), pages 1779-1799, November.

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