The paper examines three equity-based structural models to study the nonlinear relationship between equity and credit default swap (CDS) prices. These models differ in the specification of the default barrier. With cross-firm CDS premia and equity information, we are able to estimate and compare the three models. We find that the stochastic barrier model performs better than the constant and uncertain barrier models in terms of both in-sample fit and out-of-sample forecasting of CDS premia. In addition, we demonstrate a linkage between the default barrier, jump intensity, and barrier volatility estimated from our models and firm-specific variables related to default risk, such as credit ratings, equity volatility, and leverage ratios.