We study whether option-implied jump risk premia can explain the high observed level of credit spreads (the `credit spread puzzle'). We use a structural jump-diffusion firm value model with systematic and firm-specific jumps to assess the level of credit spreads that is generated by option-implied jump risk premia. In our compound option pricing model, an equity index option is an option on a portfolio of call options on the underlying firm values. Prices and returns of equity index and individual put options are used to estimate the jump parameters. We further calibrate the model parameters to historical information on default risk and the equity premium. Our results show that incorporating option-implied jump risk premia brings predicted credit spread levels much closer to observed levels. The introduction of jumps also produces model predictions for the volatility of credit spread changes and equity returns that are closer to the empirically observed values and generates a reasonable fit of observed default correlations.