Volatilities and Correlations in the Stock Market During the Global Financial Crisis

This paper investigates the behaviour of volatilities and correlations in the U.S. stock market before, during and after the Global Financial Crisis of 2007-08. We study their nature using the DJIA index and its components for the period 21/11/2005-23/9/2012 by plotting the trajectories and transforming the returns series into visibility graphs and correlation networks. We observe volatility clustering of various forms in the time series of returns and uncover regular fluctuations in market correlations. We study the degree distributions of the visibility graphs and find that they agree with the scale-free property that has been found for many naturally occurring complex networks. Minimal spanning trees on the correlation networks allow the market to be interpreted as an integrated whole. Our approach allows us to analyze empirical observations with network theory. As market dynamics is complex, the use of graphical methods, which have been fruitfully employed to the study of complex networks, provides a new perspective in the interpretation of financial data