恐慌时期的统计特征：作为自组织系统的市场
Statistical Signatures in Times of Panic: Markets as a Self-Organizing System
摘要：
我们研究收益率的横截面分布的性质。分散度和横截面峰度之间存在显著的反相关性，在恐慌时期，分散度高，但峰度低，而在正常时期则相反。在恐慌时期，股票收益的联动性也会增加。我们定义了一个简单的统计量$s$，即给定日期收益率符号的归一化和，以捕获系统中的相关程度。$s$可以被看作是系统的序参量，因为如果$s= 0$没有相关性（无序状态），而对于$s \ne 0$，股票之间存在相关性（有序状态）。我们做了一个类比，非平衡相变和假设，金融市场进行自组织时，外部波动的感知上升到某个临界值以上。事实上，$s$的分布在正常时期是单峰的，在恐慌时期转变为双峰。这与二阶相变是一致的。股票的联合随机过程的模拟在时间方向上使用多时间尺度过程和用于截面相关性的动态的序参数$s$的方程。数值结果表明，在正常和恐慌时期，与真实数据的程式化事实有很好的定性一致性。
英文摘要：
We study properties of the cross-sectional distribution of returns. A significant anti-correlation between dispersion and cross-sectional kurtosis is found such that dispersion is high but kurtosis is low in panic times, and the opposite in normal times. The co-movement of stock returns also increases in panic times. We define a simple statistic $s$, the normalized sum of signs of returns on a given day, to capture the degree of correlation in the system. $s$ can be seen as the order parameter of the system because if $s= 0$ there is no correlation (a disordered state), whereas for $s \ne 0$ there is correlation among stocks (an ordered state). We make an analogy to non-equilibrium phase transitions and hypothesize that financial markets undergo self-organization when the external volatility perception rises above some critical value. Indeed, the distribution of $s$ is unimodal in normal times, shifting to bimodal in times of panic. This is consistent with a second order phase transition. Simulations of a joint stochastic process for stocks use a multi timescale process in the temporal direction and an equation for the order parameter $s$ for the dynamics of the cross-sectional correlation. Numerical results show good qualitative agreement with the stylized facts of real data, in both normal and panic times.
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