A copula approach on the dynamics of statistical dependencies in the US stock market

We analyze the statistical dependence structure of the S&P 500 constituents in the 4-year period from 2007 to 2010 using intraday data from the New York Stock Exchange’s TAQ database. Instead of using a given parametric copula with a predetermined shape, we study the empirical pairwise copula directly. We find that the shape of this copula resembles the Gaussian copula to some degree, but exhibits a stronger tail dependence, for both correlated and anti-correlated extreme events. By comparing the tail dependence dynamically to the market’s average correlation level as a commonly used quantity we disclose the average level of error of the Gaussian copula, which is implied in the calculation of many correlation coefficients.