英文标题：
《Unravelling the trading invariance hypothesis》
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作者：
Michael Benzaquen, Jonathan Donier, Jean-Philippe Bouchaud
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最新提交年份：
2016
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英文摘要：
We confirm and substantially extend the recent empirical result of Andersen et al. \\cite{Andersen2015}, where it is shown that the amount of risk $W$ exchanged in the E-mini S\\&P futures market (i.e. price times volume times volatility) scales like the 3/2 power of the number of trades $N$. We show that this 3/2-law holds very precisely across 12 futures contracts and 300 single US stocks, and across a wide range of time scales. However, we find that the \"trading invariant\" $I=W/N^{3/2}$ proposed by Kyle and Obizhaeva is in fact quite different for different contracts, in particular between futures and single stocks. Our analysis suggests $I/{\\cal C}$ as a more natural candidate, where $\\cal C$ is the average spread cost of a trade, defined as the average of the trade size times the bid-ask spread. We also establish two more complex scaling laws for the volatility $\\sigma$ and the traded volume $V$ as a function of $N$, that reveal the existence of a characteristic number of trades $N_0$ above which the expected behaviour $\\sigma \\sim \\sqrt{N}$ and $V \\sim N$ hold, but below which strong deviations appear, induced by the size of the~tick.
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中文摘要：
我们确认并大幅扩展了Andersen等人最近的实证结果。{Andersen 2015}，其中表明，在E-mini S\\&P期货市场（即价格乘以成交量乘以波动率）中交换的风险$W$金额，与交易数量的3/2幂次方$N$类似。我们证明了这一3/2定律在12个期货合约和300只美国股票以及广泛的时间尺度上都非常精确。然而，我们发现Kyle和Obizhaeva提出的“交易不变量”$I=W/N^{3/2}$对于不同的合同，尤其是期货和单一股票之间的合同，实际上是完全不同的。我们的分析表明$I/{\\cal C}$是一个更自然的候选者，其中$\\cal C$是交易的平均差价成本，定义为交易规模乘以买卖差价的平均值。我们还为波动率$\\sigma$和交易量$V$建立了两个更复杂的标度律，作为$\\N$的函数，这揭示了存在一个特征数量的交易$\\N$，高于此数量，预期行为$\\sigma\\sim\\sqrt{N}$和$\\V\\sim N$保持不变，但低于此数量，则会出现强烈的偏差，这是由~tick的大小引起的。
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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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