英文标题：
《Theoretical and empirical analysis of trading activity》
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作者：
Mathias Pohl and Alexander Ristig and Walter Schachermayer and Ludovic
  Tangpi
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最新提交年份：
2018
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英文摘要：
  Understanding the structure of financial markets deals with suitably determining the functional relation between financial variables. In this respect, important variables are the trading activity, defined here as the number of trades $N$, the traded volume $V$, the asset price $P$, the squared volatility $\\sigma^2$, the bid-ask spread $S$ and the cost of trading $C$. Different reasonings result in simple proportionality relations (\"scaling laws\") between these variables. A basic proportionality is established between the trading activity and the squared volatility, i.e., $N \\sim \\sigma^2$. More sophisticated relations are the so called 3/2-law $N^{3/2} \\sim \\sigma P V /C$ and the intriguing scaling $N \\sim (\\sigma P/S)^2$. We prove that these \"scaling laws\" are the only possible relations for considered sets of variables by means of a well-known argument from physics: dimensional analysis. Moreover, we provide empirical evidence based on data from the NASDAQ stock exchange showing that the sophisticated relations hold with a certain degree of universality. Finally, we discuss the time scaling of the volatility $\\sigma$, which turns out to be more subtle than one might naively expect.
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中文摘要：
理解金融市场的结构需要适当地确定金融变量之间的函数关系。在这方面，重要变量是交易活动，此处定义为交易数量N$、交易量V$、资产价格P$、波动率平方$\\sigma^2$、买卖价差S$和交易成本C$。不同的推理导致这些变量之间存在简单的比例关系（“比例定律”）。在交易活动和平方波动率之间建立了一个基本的比例关系，即$N\\sim\\sigma^2$。更复杂的关系是所谓的3/2定律$N^{3/2}\\Sima P V/C$和有趣的缩放$N\\sim（\\sigma P/S）^2$。我们通过物理学中一个著名的论点：量纲分析，证明了这些“标度律”是所考虑的变量集的唯一可能的关系。此外，我们基于纳斯达克证券交易所的数据提供了经验证据，表明复杂的关系具有一定的普遍性。最后，我们讨论了波动率$\\sigma$的时间标度，这比人们天真地预期的要微妙得多。
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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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