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

The trade size omega 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 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 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 similar to omega(alpha) with alpha approximate to 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 alpha = alpha(omega)/alpha(r) is verified for some individual stocks and for the whole data set containing all stocks using partially filled trades, 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.