英文标题：
《Beyond the square root: Evidence for logarithmic dependence of market
impact on size and participation rate》
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作者：
Elia Zarinelli, Michele Treccani, J. Doyne Farmer, Fabrizio Lillo
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最新提交年份：
2014
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英文摘要：
We make an extensive empirical study of the market impact of large orders (metaorders) executed in the U.S. equity market between 2007 and 2009. We show that the square root market impact formula, which is widely used in the industry and supported by previous published research, provides a good fit only across about two orders of magnitude in order size. A logarithmic functional form fits the data better, providing a good fit across almost five orders of magnitude. We introduce the concept of an \"impact surface\" to model the impact as a function of both the duration and the participation rate of the metaorder, finding again a logarithmic dependence. We show that during the execution the price trajectory deviates from the market impact, a clear indication of non-VWAP executions. Surprisingly, we find that sometimes the price starts reverting well before the end of the execution. Finally we show that, although on average the impact relaxes to approximately 2/3 of the peak impact, the precise asymptotic value of the price depends on the participation rate and on the duration of the metaorder. We present evidence that this might be due to a herding phenomenon among metaorders.
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中文摘要：
我们对2007年至2009年间美国股市执行的大订单（元订单）的市场影响进行了广泛的实证研究。我们表明，平方根市场影响公式在行业中得到广泛应用，并得到了之前发表的研究的支持，它仅在订单规模的两个数量级上提供了良好的拟合。对数函数形式更适合数据，在几乎五个数量级上提供了良好的拟合。我们引入“影响面”的概念，将影响建模为元序的持续时间和参与率的函数，再次发现对数相关性。我们表明，在执行期间，价格轨迹偏离了市场影响，这是非VWAP执行的明确迹象。令人惊讶的是，我们发现有时价格在执行结束之前就开始回升。最后，我们表明，虽然平均而言，影响放松到峰值影响的约2/3，但价格的精确渐近值取决于参与率和元序的持续时间。我们提出的证据表明，这可能是由于元目之间的羊群现象。
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分类信息：

一级分类：Quantitative Finance 数量金融学
二级分类：Trading and Market Microstructure 交易与市场微观结构
分类描述：Market microstructure, liquidity, exchange and auction design, automated trading, agent-based modeling and market-making
市场微观结构，流动性，交易和拍卖设计，自动化交易，基于代理的建模和做市
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