A theory of power-law distributions in financial market fluctuations

Gabaix X.; Gopikrishnan P.; Plerou V.; Stanley HE.

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A theory of power-law distributions in financial market fluctuations

机译：金融市场波动中的幂律分布理论

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Insights into the dynamics of a complex system are often gained by focusing on large fluctuations. For the financial system, huge databases now exist that facilitate the analysis of large fluctuations and the characterization of their statistical behaviour(1,2). Power laws appear to describe histograms of relevant financial fluctuations, such as fluctuations in stock price, trading volume and the number of trades(3-10). Surprisingly, the exponents that characterize these power laws are similar for different types and sizes of markets, for different market trends and even for different countries - suggesting that a generic theoretical basis may underlie these phenomena. Here we propose a model, based on a plausible set of assumptions, which provides an explanation for these empirical power laws. Our model is based on the hypothesis that large movements in stock market activity arise from the trades of large participants. Starting from an empirical characterization of the size distribution of those large market participants ( mutual funds), we show that the power laws observed in financial data arise when the trading behaviour is performed in an optimal way. Our model additionally explains certain striking empirical regularities that describe the relationship between large fluctuations in prices, trading volume and the number of trades. [References: 28]

机译：通常，通过关注较大的波动，可以深入了解复杂系统的动力学。对于金融系统而言，现在存在着巨大的数据库，可以方便地分析大的波动并表征其统计行为（1,2）。幂律似乎描述了相关金融波动的直方图，例如股价，交易量和交易次数的波动（3-10）。出乎意料的是，对于不同类型和大小的市场，不同市场趋势甚至不同国家而言，表征这些幂定律的指数都是相似的，这表明这些现象可能是通用的理论基础。在这里，我们提出了一个基于一组合理假设的模型，该模型为这些经验幂定律提供了解释。我们的模型基于这样的假设，即股票市场活动的大幅波动是由大型参与者的交易引起的。从那些大型市场参与者（共同基金）的规模分布的经验表征开始，我们表明，当以最佳方式执行交易行为时，金融数据中观察到的幂定律就会出现。我们的模型还解释了一些惊人的经验规律，这些规律描述了价格，交易量和交易数量的大幅度波动之间的关系。 [参考：28]

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《Nature》 |2003年第6937期|p. 267-270|共4页
作者
Gabaix X.; Gopikrishnan P.; Plerou V.; Stanley HE.;
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收录信息美国《科学引文索引》(SCI);美国《工程索引》(EI);美国《生物学医学文摘》(MEDLINE);美国《化学文摘》(CA);
原文格式 PDF
正文语种 eng
中图分类自然科学总论;
关键词
Statistical properties; Price fluctuations; Zipfs law; Trades; Companies;

机译：统计属性;价格波动;齐普夫定律;交易;公司介绍;

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专利

1. EMERGENCE OF POWER-LAW AND TWO-PHASE BEHAVIOR IN FINANCIAL MARKET FLUCTUATIONS [J] . ZVONKO KOSTANJ?AR, BRANKO JEREN Advances in complex systems . 2013,第1期

机译：金融市场波动中幂律和两相行为的出现
2. On the scaling of the distribution of daily price fluctuations in the Mexican financial market index [J] . Alfonso L., Mansilla R., Terrero-Escalante C.A. Physica, A. Statistical mechanics and its applications . 2012,第10期

机译：关于每日价格波动分布在墨西哥金融市场指数中的缩放比例
3. Scaling of the distribution of fluctuations of financial market indices [J] . Gopikrishnan P., Amaral LAN., Meyer M., Physical review, E. Statistical physics, plasmas, fluids, and related interdisciplinary topics . 1999,第5aPta1期

机译：缩放金融市场指数波动的分布
4. Applying Market Profile Theory to Analyze Financial Big Data and Discover Financial Market Trading Behavior - A Case Study of Taiwan Futures Market [C] . Wei-Yuan Huang, An-Pin Chen, Yu-Hsiang Hsu, International Conference on Cloud Computing and Big Data . 2016

机译：应用市场概况理论分析金融大数据并发现金融市场交易行为-以台湾期货市场为例
5. Sovereign credit rating news and financial markets fluctuations: Evidence from the European market. [D] . Lai, Yun. 2013

机译：主权信用评级新闻和金融市场波动：来自欧洲市场的证据。
6. Mesoscopic Community Structure of Financial Markets Revealed by Price and Sign Fluctuations [O] . Assaf Almog, Ferry Besamusca, Mel MacMahon, -1

机译：价格和符号波动揭示了金融市场的介观社区结构
7. Financial Development and the Distributional Effects of Monetary Policy Do the distributional consequences of monetary policy depend on the extent of financial development? Should optimal monetary policy vary across countries? In order to answer these questions, we develop a monetary growth production model with heterogeneous agents. In our economy, optimal policy needs to weigh the effects of policy across two groups — capital owners and individuals who hold liquid assets. While banks help limit the exposure to inflation, there are limits because money alleviates the frictions of private information and limited communication. In this environment, we compare two economies that are identical in every aspect except for their level of financial development. In a country with limited financial development, a stock market is absent. In the other, an equity market is active. In either economy, inflation adversely affects capital formation and output. Individuals who hold liquid assets are always adversely affected by inflation, but the attitude of capital owners depends on the level of financial development. In particular, in the presence of a stock market, the impact of inflation on the welfare of capital owners is non-monotonic. Nevertheless, optimal monetary policy is always more conservative at higher levels of financial development. [O] . TINA M. Edgar A. Ghossoub, TINA M. Robert R. Reedy 100

机译：金融发展和货币政策的分配效应货币政策的分配后果是否取决于金融发展的程度？各国的最优货币政策应该不同吗？为了回答这些问题，我们开发了一个具有异构代理的货币增长生产模型。在我们的经济中，最优政策需要权衡两个群体的政策效应 - 资本所有者和持有流动资产的个人。虽然银行帮助限制通胀风险，但存在限制，因为资金减轻了私人信息的摩擦和有限的沟通。在这种环境下，我们比较两个经济体在各个方面都是相同的，除了它们的金融发展水平。在金融发展有限的国家，缺乏股票市场。另一方面，股票市场活跃。在任一经济体中，通胀都会对资本形成和产出产生不利影响持有流动资产的个人总是受到通货膨胀的不利影响，但资本所有者的态度取决于金融发展的水平。特别是，在股票市场存在的情况下，通货膨胀对资本所有者福利的影响是非单调的。尽管如此，在较高的金融发展水平下，最优货币政策总是更加保守。

A theory of power-law distributions in financial market fluctuations

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