摘要翻译：
许多研究假设股票价格遵循一个被称为几何布朗运动的随机过程。尽管这一模型大致正确，但它无法解释极端价格波动的频繁发生，如股市崩盘。利用来自三个不同股票市场的大量数据，我们提供了证据，证明对随机模型的修改--在过程的标准差中增加一个缓慢但显著的波动--准确地解释了不同规模价格变化的概率，包括极端运动的相对高频率。此外，我们还证明了这一过程在股票上是相似的，因此它们的价格波动可以用一条单一的曲线来表征。由于价格波动的行为植根于波动性的特征，我们期望我们的结果能给随机波动性模型带来更多的兴趣，特别是那些能产生本文报告的波动性性质的模型。
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英文标题：
《Universal Behavior of Extreme Price Movements in Stock Markets》
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作者：
Miguel A. Fuentes, Austin Gerig, and Javier Vicente
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最新提交年份：
2009
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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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英文摘要：
  Many studies assume stock prices follow a random process known as geometric Brownian motion. Although approximately correct, this model fails to explain the frequent occurrence of extreme price movements, such as stock market crashes. Using a large collection of data from three different stock markets, we present evidence that a modification to the random model -- adding a slow, but significant, fluctuation to the standard deviation of the process -- accurately explains the probability of different-sized price changes, including the relative high frequency of extreme movements. Furthermore, we show that this process is similar across stocks so that their price fluctuations can be characterized by a single curve. Because the behavior of price fluctuations is rooted in the characteristics of volatility, we expect our results to bring increased interest to stochastic volatility models, and especially to those that can produce the properties of volatility reported here.
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PDF链接：
https://arxiv.org/pdf/0912.5448