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

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• Wei-Xing Zhou

(ECUST)

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Abstract

The trade size $\omega$ has 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 $\omega$ 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 impact. 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 $r\sim \omega^\alpha$ with $\alpha\approx2/3$. 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 $\alpha=\alpha_\omega/\alpha_r$ is verified, where $\alpha_\omega$ and $\alpha_r$ are the tail exponents of trade sizes and returns. These observations also enable us to explain the anomalous negative correlation between $r$ and $\omega$ for small-size trades. We anticipate that these regularities may hold in other order-driven markets.

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File URL: http://arxiv.org/pdf/0708.3198

Bibliographic Info

Paper provided by arXiv.org in its series Papers with number 0708.3198.

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 Length: Date of creation: Aug 2007 Date of revision: Apr 2008 Publication status: Published in Quantitative Finance 12 (8), 1253-1263 (2012) Handle: RePEc:arx:papers:0708.3198 Contact details of provider: Web page: http://arxiv.org/

References

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1. V. Plerou & P. Gopikrishnan & L. A. N. Amaral & M. Meyer & H. E. Stanley, 1999. "Scaling of the distribution of price fluctuations of individual companies," Papers cond-mat/9907161, arXiv.org.
2. Xavier Gabaix & Parameswaran Gopikrishnan & Vasiliki Plerou & H. Eugene Stanley, 2007. "A Theory of Limited Liquidity and Large Investors Causing Spikes in Stock Market Volatility and Trading Volume," Journal of the European Economic Association, MIT Press, vol. 5(2-3), pages 564-573, 04-05.
3. 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.
4. Bouchaud, Jean-Philippe & Potters, Marc, 2001. "More stylized facts of financial markets: leverage effect and downside correlations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 299(1), pages 60-70.
5. Epps, Thomas W & Epps, Mary Lee, 1976. "The Stochastic Dependence of Security Price Changes and Transaction Volumes: Implications for the Mixture-of-Distributions Hypothesis," Econometrica, Econometric Society, vol. 44(2), pages 305-21, March.
6. Eisler, Zoltán & Kertész, János, 2007. "The dynamics of traded value revisited," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 382(1), pages 66-72.
7. Marc Potters & Jean-Philippe Bouchaud, 2001. "More stylized facts of financial markets: leverage effect and downside correlations," Science & Finance (CFM) working paper archive 29960, Science & Finance, Capital Fund Management.
8. 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.
9. Karpoff, Jonathan M., 1987. "The Relation between Price Changes and Trading Volume: A Survey," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 22(01), pages 109-126, March.
10. Zoltan Eisler & Janos Kertesz, 2005. "Size matters: some stylized facts of the stock market revisited," Papers physics/0508156, arXiv.org, revised May 2006.
11. Jain, Prem C. & Joh, Gun-Ho, 1988. "The Dependence between Hourly Prices and Trading Volume," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 23(03), pages 269-283, September.
12. Lee, Kyoung Eun & Lee, Jae Woo, 2007. "Probability distribution function and multiscaling properties in the Korean stock market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 383(1), pages 65-70.
13. Sergei Maslov & Mark Mills, 2001. "Price fluctuations from the order book perspective - empirical facts and a simple model," Papers cond-mat/0102518, arXiv.org.
14. Z. Eisler & J. Kertész, 2006. "Size matters: some stylized facts of the stock market revisited," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 51(1), pages 145-154, 05.
15. Gabaix, Xavier & Gopikrishnan, Parameswaran & Plerou, Vasiliki & Stanley, H.Eugene, 2003. "Understanding the cubic and half-cubic laws of financial fluctuations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 324(1), pages 1-5.
16. 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.
17. Gabaix, Xavier & Gopikrishnan, Parameswaran & Plerou, Vasiliki & Eugene Stanley, H., 2008. "Quantifying and understanding the economics of large financial movements," Journal of Economic Dynamics and Control, Elsevier, vol. 32(1), pages 303-319, January.
18. Parameswaran Gopikrishnan & Vasiliki Plerou & Luis A. Nunes Amaral & Martin Meyer & H. Eugene Stanley, 1999. "Scaling of the distribution of fluctuations of financial market indices," Papers cond-mat/9905305, arXiv.org.
19. Chan, Kalok & Fong, Wai-Ming, 2000. "Trade size, order imbalance, and the volatility-volume relation," Journal of Financial Economics, Elsevier, vol. 57(2), pages 247-273, August.
20. Harris, Lawrence, 1987. "Transaction Data Tests of the Mixture of Distributions Hypothesis," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 22(02), pages 127-141, June.
21. Xavier Gabaix & Parameswaran Gopikrishnan & Vasiliki Plerou & H. Eugene Stanley, 2005. "Institutional Investors and Stock Market Volatility," NBER Working Papers 11722, National Bureau of Economic Research, Inc.
22. V. Plerou & P. Gopikrishnan & X. Gabaix & L. A. N. Amaral & H. E. Stanley, 2001. "Price fluctuations, market activity and trading volume," Quantitative Finance, Taylor & Francis Journals, vol. 1(2), pages 262-269.
23. J. Doyne Farmer & Fabrizio Lillo, 2003. "On the origin of power law tails in price fluctuations," Papers cond-mat/0309416, arXiv.org, revised Jan 2004.
24. Naes, Randi & Skjeltorp, Johannes A., 2006. "Order book characteristics and the volume-volatility relation: Empirical evidence from a limit order market," Journal of Financial Markets, Elsevier, vol. 9(4), pages 408-432, November.
25. Saatcioglu, Kemal & Starks, Laura T., 1998. "The stock price-volume relationship in emerging stock markets: the case of Latin America," International Journal of Forecasting, Elsevier, vol. 14(2), pages 215-225, June.
26. Jean-Philippe Bouchaud & Yuval Gefen & Marc Potters & Matthieu Wyart, 2003. "Fluctuations and response in financial markets: the subtle nature of `random' price changes," Papers cond-mat/0307332, arXiv.org, revised Aug 2003.
27. Damien Challet & Robin Stinchcombe, 2001. "Analyzing and modelling 1+1d markets," Papers cond-mat/0106114, arXiv.org, revised Jun 2001.
28. Zoltan Eisler & Janos Kertesz, 2006. "The dynamics of traded value revisited," Papers physics/0608018, arXiv.org, revised Mar 2007.
29. P. Gopikrishnan & M. Meyer & L.A.N. Amaral & H.E. Stanley, 1998. "Inverse cubic law for the distribution of stock price variations," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 3(2), pages 139-140, July.
30. Rogalski, Richard J, 1978. "The Dependence of Prices and Volume," The Review of Economics and Statistics, MIT Press, vol. 60(2), pages 268-74, May.
31. Vasiliki Plerou & Parameswaran Gopikrishnan & Xavier Gabaix & H. Eugene Stanley, 2004. "On the Origin of Power-Law Fluctuations in Stock Prices," Papers cond-mat/0403067, arXiv.org.
32. Clark, Peter K, 1973. "A Subordinated Stochastic Process Model with Finite Variance for Speculative Prices," Econometrica, Econometric Society, vol. 41(1), pages 135-55, January.
33. Epps, Thomas W, 1975. "Security Price Changes and Transaction Volumes: Theory and Evidence," American Economic Review, American Economic Association, vol. 65(4), pages 586-97, September.
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