Random matrix application to correlations amongst the volatility of assets

Ajay Singh and Dinghai Xu

Quantitative Finance, 2016, vol. 16, issue 1, 69-83

Abstract: In this paper, we apply tools from random matrix theory (RMT) to estimates of correlations across the volatility of various assets in the S&P 500. The volatility inputs are estimated by modelling price fluctuations as a GARCH(1,1) process. The corresponding volatility correlation matrix is then constructed. It is found that the distribution of a significant number of eigenvalues of the volatility correlation matrix matches with the analytical result from RMT. Furthermore, the empirical estimates of short- and long-range correlations amongst eigenvalues, which are within RMT bounds, match with the analytical results for the Gaussian Orthogonal ensemble of RMT. To understand the information content of the largest eigenvectors, we estimate the contribution of the Global Industry Classification Standard industry groups to each eigenvector. In comparison with eigenvectors of correlation matrix for price fluctuations, only few of the largest eigenvectors of the volatility correlation matrix are dominated by a single industry group. We also study correlations between ‘volatility returns’ and log-volatility to find similar results.

Date: 2016
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Working Paper: Random Matrix Application to Correlations Among Volatility of Assets (2013)
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DOI: 10.1080/14697688.2015.1014400

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