首次通过时间概率的标度性质和普适性 在金融市场

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摘要翻译：
金融市场为研究非高斯相关动力学的交叉或首次通过时间事件提供了一个理想的框架，这主要是因为金融市场拥有大量的数据集。本文考虑了六个期货市场的逐滴答数据，导致了胖尾首次通过时间概率。用标准差对收益率进行的缩放将所有被检验的市场的概率，以及不同时间范围的概率，折叠成单一曲线，表明首次通过统计是独立于市场的（至少对于高频数据是如此）。另一方面，一个非常密切相关的量，即生存概率，在离开分布的中心和尾部时，显示出一个典型的马尔科夫动力学的双曲$t^{-1/2}$衰减，尽管市场中存在记忆。Weibull分布和Study分布的修正是在一定条件下首次通过时间性质的现象学描述的很好的候选者。所示的规模策略可能对风险控制和算法交易有用。
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英文标题：
《Scaling properties and universality of first-passage time probabilities
  in financial markets》
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作者：
Josep Perell\'o, Mario Guti\'errez-Roig, Jaume Masoliver
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最新提交年份：
2011
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分类信息：

一级分类：Quantitative Finance        数量金融学
二级分类：Statistical Finance        统计金融
分类描述：Statistical, econometric and econophysics analyses with applications to financial markets and economic data
统计、计量经济学和经济物理学分析及其在金融市场和经济数据中的应用
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一级分类：Physics        物理学
二级分类：Mathematical Physics        数学物理
分类描述：Articles in this category focus on areas of research that illustrate the application of mathematics to problems in physics, develop mathematical methods for such applications, or provide mathematically rigorous formulations of existing physical theories. Submissions to math-ph should be of interest to both physically oriented mathematicians and mathematically oriented physicists; submissions which are primarily of interest to theoretical physicists or to mathematicians should probably be directed to the respective physics/math categories
这一类别的文章集中在说明数学在物理问题中的应用的研究领域，为这类应用开发数学方法，或提供现有物理理论的数学严格公式。提交的数学-PH应该对物理方向的数学家和数学方向的物理学家都感兴趣；主要对理论物理学家或数学家感兴趣的投稿可能应该指向各自的物理/数学类别
--
一级分类：Mathematics        数学
二级分类：Mathematical Physics        数学物理
分类描述：math.MP is an alias for math-ph. Articles in this category focus on areas of research that illustrate the application of mathematics to problems in physics, develop mathematical methods for such applications, or provide mathematically rigorous formulations of existing physical theories. Submissions to math-ph should be of interest to both physically oriented mathematicians and mathematically oriented physicists; submissions which are primarily of interest to theoretical physicists or to mathematicians should probably be directed to the respective physics/math categories
math.mp是math-ph的别名。这一类别的文章集中在说明数学在物理问题中的应用的研究领域，为这类应用开发数学方法，或提供现有物理理论的数学严格公式。提交的数学-PH应该对物理方向的数学家和数学方向的物理学家都感兴趣；主要对理论物理学家或数学家感兴趣的投稿可能应该指向各自的物理/数学类别
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一级分类：Physics        物理学
二级分类：Data Analysis, Statistics and Probability        数据分析、统计与概率
分类描述：Methods, software and hardware for physics data analysis: data processing and storage; measurement methodology; statistical and mathematical aspects such as parametrization and uncertainties.
物理数据分析的方法、软硬件：数据处理与存储；测量方法；统计和数学方面，如参数化和不确定性。
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英文摘要：
  Financial markets provide an ideal frame for the study of crossing or first-passage time events of non-Gaussian correlated dynamics mainly because large data sets are available. Tick-by-tick data of six futures markets are herein considered resulting in fat tailed first-passage time probabilities. The scaling of the return with the standard deviation collapses the probabilities of all markets examined, and also for different time horizons, into single curves, suggesting that first-passage statistics is market independent (at least for high-frequency data). On the other hand, a very closely related quantity, the survival probability, shows, away from the center and tails of the distribution, a hyperbolic $t^{-1/2}$ decay typical of a Markovian dynamics albeit the existence of memory in markets. Modifications of the Weibull and Student distributions are good candidates for the phenomenological description of first-passage time properties under certain regimes. The scaling strategies shown may be useful for risk control and algorithmic trading.
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PDF链接：
https://arxiv.org/pdf/1107.1174

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关键词：金融市场 Mathematical Applications distribution formulations 胖尾 标准差 缩放 离开 可能