Random Matrix Application to Correlations Among Volatility of Assets
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.