Dependence structure between the credit default swap return and the kurtosis of the equity return distribution: Evidence from Japan

We examine the dependence structure between the credit default swap (CDS) return and the kurtosis of the corresponding equity return distribution using copula functions to specify its nonnormal and nonlinear relationship. Three candidates, the Gaussian, the Student's t, and the Gumbel copulas, are compared. Daily CDS rates of 46 reference entities are collected from the Tokyo International Financial Exchange covering the period from April 2004 to June 2005. Our empirical results suggest that in lower rating classes, the Gumbel copula is the best fitting model, followed by the Student's t. The dependence structure is positive and asymmetric. To compensate for the higher risk, possibly incurred by more jumps, protection sellers demand higher CDS returns. Meanwhile, the upper tail dependence becomes significant as jump events and CDS returns increase simultaneously. Finally, CDS returns in lower rating classes are more sensitive to jump risk than those in the higher ratings.