This paper examines some empirical evidence related to the common assumption made in credit default risk modelling where correlation is usually presumed to be constant. Using CDS Spread indices from the liquid and efficient markets of credit derivatives, we consider an example of two car manufacturers, General Motors and Ford and show that correlation between the credit indices of these two companies is stochastic. Further analysis shows that in fact correlation process is stationary and fits normal distribution well. Under the assumption of normality, we extend the version of the structural model proposed by Hull, Predescu and White (2005) to account for stochastic correlation.