A structural model with stochastic volatility and jumps implies specific relationships between observed equity returns and credit spreads. This paper explores such effects in the credit default swap (CDS) market. We use a novel approach to identify the realized jumps of individual equities from high frequency data. Our empirical results suggest that volatility risk alone predicts 50 percent of the variation in CDS spreads, while jump risk alone forecasts 19 percent. After controlling for credit ratings, macroeconomic conditions, and firms' balance sheet information, we can explain 77 percent of the total variation. Moreover, the pricing effects of volatility and jump measures vary consistently across investment-grade and high-yield entities. The estimated nonlinear effects of volatility and jumps are in line with the model-implied relationships between equity returns and credit spreads.