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

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^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.

Keywords:

• Econophysics
• Price impact function
• Price-volume relation
• Scaling laws
• Data collapsing

Acknowledgements

I am grateful to Didier Sornette and Liang Guo for valuable discussions, Wei Chen for kindly providing the data, and Gao-Feng Gu for preprocessing the data. I also thank the referees for their insightful suggestions. This work was partially supported by the ‘Shu Guang’ project sponsored by the Shanghai Municipal Education Commission and the Shanghai Education Development Foundation (grant No. 2008SG29), Fundamental Research Funds for the Central Universities, and the Program for New Century Excellent Talents in University sponsored by the Ministry of Education of the People's Republic of China (grant No. NCET-07-0288).

Notes

†Chinese stock markets were/are very different from developed Western markets in many aspects. In 2003, only limit orders were allowed to be submitted. There were no ‘true’ market orders. This applies to all stocks, not only to the stocks studied in this paper.