Structural models of default establish a relation across the fair values of various asset classes (equity, bonds, credit derivatives) referring to the same company. In most circumstances such relation is verified in practice, as different financial assets tend to move in the same direction at similar speed. However, occasional deviations from the theoretical fair values occur, especially in times of financial turmoil. Understanding how the dynamics of the theoretical fair values of various assets compares to that of their market values is crucial to a number of market participants. This paper investigates whether a popular structural model, the CreditGrades approach proposed by Finger (2002), Stamicar and Finger (2005), succeeds in explaining the dynamic relation between equity/option variables and Credit Default Swap (CDS) premia at individual company level. We find that CDS model spreads display a significant correlation with CDS market spreads. However, the gap between the two is time varying and widens substantially in times of financial turbulence. The analysis of the gap dynamics reveals that this is partly due to episodes of decoupling between equity and credit markets, and partly due to shortcomings of the model. Finally, we observe that model spreads tend to predict market spreads.