  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.
