Santa Fe Institute, Santa Fe, New Mexico, United States of America.
PLoS One. 2009 Dec 23;4(12):e8243. doi: 10.1371/journal.pone.0008243.
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.
许多研究都假设股票价格遵循一种随机过程，称为几何布朗运动。虽然这个模型大致上是正确的，但它无法解释极端价格波动的频繁发生，如股市崩盘。我们使用来自三个不同股票市场的大量数据，提出了证据表明对随机模型的修改——为过程的标准偏差添加一个缓慢但显著的波动——可以准确地解释不同大小的价格变化的概率，包括极端波动的相对高频率。此外，我们表明，这个过程在股票之间是相似的，因此它们的价格波动可以用一条单一的曲线来描述。由于价格波动的行为源于波动性的特征，我们预计我们的结果将增加对随机波动性模型的兴趣，特别是对那些能够产生这里报告的波动性特性的模型。
