英文标题：
《Random Matrix Application to Correlations Among Volatility of Assets》
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作者：
Ajay Singh and Dinghai Xu
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最新提交年份：
2013
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英文摘要：
In this paper, we apply tools from the random matrix theory (RMT) to estimates of correlations across volatility of various assets in the S&P 500. The volatility inputs are estimated by modeling price fluctuations as GARCH(1,1) process. The corresponding correlation matrix is constructed. It is found that the distribution of a significant number of eigenvalues of the volatility correlation matrix matches with the analytical result from the RMT. Furthermore, the empirical estimates of short and long-range correlations among eigenvalues, which are within the RMT bounds, match with the analytical results for Gaussian Orthogonal ensemble (GOE) of the RMT. To understand the information content of the largest eigenvectors, we estimate the contribution of GICS industry groups in each eigenvector. In comparison with eigenvectors of correlation matrix for price fluctuations, only few of the largest eigenvectors of volatility correlation matrix are dominated by a single industry group. We also study correlations among `volatility return\' and get similar results.
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中文摘要：
在本文中，我们应用随机矩阵理论（RMT）中的工具来估计标准普尔500指数中各种资产的波动性之间的相关性。通过将价格波动建模为GARCH（1,1）过程来估计波动性输入。构造了相应的相关矩阵。研究发现，波动率相关矩阵的大量特征值的分布与RMT的分析结果相匹配。此外，在RMT范围内的特征值之间的短期和长期相关性的经验估计与RMT的高斯正交系综（GOE）的分析结果相匹配。为了了解最大特征向量的信息含量，我们估计了GICS行业组在每个特征向量中的贡献。与价格波动相关矩阵的特征向量相比，波动相关矩阵的最大特征向量中只有少数由单个行业组主导。我们还研究了“波动率-收益率”之间的相关性，得到了类似的结果。
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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：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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一级分类：Quantitative Finance 数量金融学
二级分类：Risk Management 风险管理
分类描述：Measurement and management of financial risks in trading, banking, insurance, corporate and other applications
衡量和管理贸易、银行、保险、企业和其他应用中的金融风险
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一级分类：Quantitative Finance 数量金融学
二级分类：Trading and Market Microstructure 交易与市场微观结构
分类描述：Market microstructure, liquidity, exchange and auction design, automated trading, agent-based modeling and market-making
市场微观结构，流动性，交易和拍卖设计，自动化交易，基于代理的建模和做市
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