Changing default risk dependencies during the subprime crisis: DJ iTraxx subindices and goodness-of-fit-testing for copulas

Abstract

This paper tests whether (and to what extent) default risk dependencies changed during the subprime crisis in 2007 and 2008. This is done by applying a Goodness-of-fit test, based on the Rosenblatt transformation, to test various null hypotheses with respect to the copula function that describes the stochastic dependence between daily returns of six sector-specific subindices of the Dow Jones iTraxx Credit Default Swap index for Europe. Overall, the results suggest that in the bivariate case, the t-copula is a better approximation to the true copula of returns of DJ iTraxx subindices than the normal copula or the generalized Clayton copula. On average, the number of degrees of freedom of the bivariate t-copula tends to decrease during the crisis. As expected, the correlation between the returns of the subindices increases significantly during the crisis. However, the multivariate analysis reveals that it is only before the crisis that the null hypothesis of a six-dimensional t-copula is not rejected. During the crisis, the multivariate stochastic dependence between the sector-specific DJ iTraxx subindices seems to change in such a complex way that it is no longer sufficiently described by a multivariate t-copula.