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Universal price impact functions of individual trades in an order-driven market

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  • Wei-Xing Zhou

Abstract

The trade size ω has a direct impact on the price formation of the stock traded. Econophysical analyses of transaction data for the US and Australian stock markets have uncovered market-specific scaling laws, where a master curve of price impact can be obtained in each market when stock capitalization C is included as an argument in the scaling relation. However, the rationale of introducing stock capitalization in the scaling is unclear and the anomalous negative correlation between price change r and trade size ω for small trades is unexplained. Here we show that these issues can be addressed by taking into account the aggressiveness of orders that result in trades together with a proper normalization technique. Using order book data from the Chinese market, we show that trades from filled and partially filled limit orders have very different price impacts. The price impact of trades from partially filled orders is constant when the volume is not too large, while that of filled orders shows power-law behavior r ∼ ω-super-α with α ≈ 2/3. When returns and volumes are normalized by stock-dependent averages, capitalization-independent scaling laws emerge for both types of trades. However, no scaling relation in terms of stock capitalization can be constructed. In addition, the relation α = α ω /α r is verified for some individual stocks and for the whole data set containing all stocks using partially filled trades, where α ω and α r are the tail exponents of trade sizes and returns. These observations also enable us to explain the anomalous negative correlation between r and ω for small-size trades.

Suggested Citation

  • 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.
  • Handle: RePEc:taf:quantf:v:12:y:2012:i:8:p:1253-1263
    DOI: 10.1080/14697688.2010.504733
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    Citations

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    Cited by:

    1. 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.
    2. Gao-Feng Gu & Xiong Xiong & Hai-Chuan Xu & Wei Zhang & Yong-Jie Zhang & Wei Chen & Wei-Xing Zhou, 2017. "An empirical behavioural order-driven model with price limit rules," Papers 1704.04354, arXiv.org.
    3. repec:eee:phsmap:v:483:y:2017:i:c:p:201-208 is not listed on IDEAS
    4. Jian Zhou & Gao-Feng Gu & Zhi-Qiang Jiang & Xiong Xiong & Wei Chen & Wei Zhang & Wei-Xing Zhou, 2014. "Computational experiments successfully predict the emergence of autocorrelations in ultra-high-frequency stock returns," Papers 1404.1051, arXiv.org, revised Feb 2018.
    5. Yu-Lei Wan & Gang-Jin Wang & Zhi-Qiang Jiang & Wen-Jie Xie & Wei-Xing Zhou, 2018. "The cooling-off effect of price limits in the Chinese stock markets," Papers 1803.09422, arXiv.org.
    6. 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.
    7. repec:eee:phsmap:v:493:y:2018:i:c:p:301-310 is not listed on IDEAS
    8. 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.
    9. Du, Bian & Zhu, Hongliang & Zhao, Jingdong, 2016. "Optimal execution in high-frequency trading with Bayesian learning," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 461(C), pages 767-777.
    10. Yergeau, Gabriel, 2016. "Profitability and Market Quality of High Frequency Market-makers: An Empirical Investigation," Working Papers 16-3, HEC Montreal, Canada Research Chair in Risk Management.
    11. 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.
    12. Zhang, Wei & Bi, Zhengzheng & Shen, Dehua, 2017. "Investor structure and the price–volume relationship in a continuous double auction market: An agent-based modeling perspective," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 467(C), pages 345-355.
    13. Lajbcygier, Paul & Sojka, Jeremy, 2015. "The viability of alternative indexation when including all costs," International Review of Financial Analysis, Elsevier, vol. 38(C), pages 109-141.
    14. Hasan, Rashid & Mohammed Salim, M., 2017. "Power law cross-correlations between price change and volume change of Indian stocks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 473(C), pages 620-631.
    15. Zhi-Qiang Jiang & Wen-Jie Xie & Xiong Xiong & Wei Zhang & Yong-Jie Zhang & W. -X. Zhou, 2012. "Trading networks, abnormal motifs and stock manipulation," Papers 1301.0007, arXiv.org.
    16. 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.
    17. repec:eee:phsmap:v:483:y:2017:i:c:p:266-272 is not listed on IDEAS
    18. Gao, Yan & Gao, Yao, 2015. "Statistical properties of short-selling and margin-trading activities and their impacts on returns in the Chinese stock markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 438(C), pages 293-307.
    19. repec:kap:compec:v:50:y:2017:i:4:d:10.1007_s10614-016-9612-1 is not listed on IDEAS
    20. Hai-Chuan Xu & Zhi-Qiang Jiang & Wei-Xing Zhou, 2016. "Immediate price impact of a stock and its warrant: Power-law or logarithmic model?," Papers 1611.04091, arXiv.org.
    21. T. Zhang & G. -F. Gu & H. -C. Xu & X. Xiong & W. Chen & W. -X. Zhou, 2017. "Power-law tails in the distribution of order imbalance," Papers 1707.05550, arXiv.org.
    22. Harvey, M. & Hendricks, D. & Gebbie, T. & Wilcox, D., 2017. "Deviations in expected price impact for small transaction volumes under fee restructuring," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 471(C), pages 416-426.
    23. Zhong, Li-Xin & Xu, Wen-Juan & Chen, Rong-Da & Zhong, Chen-Yang & Qiu, Tian & Shi, Yong-Dong & Wang, Li-Liang, 2016. "A generalized voter model with time-decaying memory on a multilayer network," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 458(C), pages 95-105.

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