英文标题：
《An Empirical Approach to Financial Crisis Indicators Based on Random
  Matrices》
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作者：
Antoine Kornprobst, Raphael Douady
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最新提交年份：
2017
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英文摘要：
  The aim of this work is to build financial crisis indicators based on spectral properties of the dynamics of market data. After choosing an optimal size for a rolling window, the historical market data in this window is seen every trading day as a random matrix from which a covariance and a correlation matrix are obtained. The financial crisis indicators that we have built deal with the spectral properties of these covariance and correlation matrices and they are of two kinds. The first one is based on the Hellinger distance, computed between the distribution of the eigenvalues of the empirical covariance matrix and the distribution of the eigenvalues of a reference covariance matrix representing either a calm or agitated market. The idea behind this first type of indicators is that when the empirical distribution of the spectrum of the covariance matrix is deviating from the reference in the sense of Hellinger, then a crisis may be forthcoming. The second type of indicators is based on the study of the spectral radius and the trace of the covariance and correlation matrices as a mean to directly study the volatility and correlations inside the market. The idea behind the second type of indicators is the fact that large eigenvalues are a sign of dynamic instability. The predictive power of the financial crisis indicators in this framework is then demonstrated, in particular by using them as decision-making tools in a protective-put strategy.
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中文摘要：
这项工作的目的是建立基于市场数据动态光谱特性的金融危机指标。在为滚动窗口选择最佳大小后，该窗口中的历史市场数据在每个交易日被视为一个随机矩阵，从中获得协方差和相关矩阵。我们建立的金融危机指标涉及这些协方差和相关矩阵的光谱特性，它们有两种。第一种是基于海林格距离，计算经验协方差矩阵的特征值分布和代表平静或动荡市场的参考协方差矩阵的特征值分布之间的距离。第一类指标背后的想法是，当协方差矩阵频谱的经验分布偏离海林格意义上的参考时，危机可能即将到来。第二类指标基于对谱半径和协方差及相关矩阵轨迹的研究，作为直接研究市场内部波动性和相关性的一种手段。第二类指标背后的理念是，较大的特征值是动态不稳定的迹象。然后，通过将金融危机指标用作保护性看跌期权策略的决策工具，展示了该框架中金融危机指标的预测能力。
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分类信息：

一级分类：Quantitative Finance        数量金融学
二级分类：Mathematical Finance        数学金融学
分类描述：Mathematical and analytical methods of finance, including stochastic, probabilistic and functional analysis, algebraic, geometric and other methods
金融的数学和分析方法，包括随机、概率和泛函分析、代数、几何和其他方法
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