We study new structural credit risk models that provide flexible alternatives to the well-known Black-Cox model. The defaults within our models are characterized in accordance with Chapter 7 (a liquidation process) and Chapter 11 (a reorganization process) of the U.S. Bankruptcy Code. The risk-neutral default probabilities hence involve joint probability distributions of the underlying firm value with imposed killing at the liquidation barrier and its occupation time with respect to the reorganization barrier. Occupation times are powerful tools in credit risk modelling as they correctly measure the cumulative time spent in each regime. The proposed model bases on a non-linear state-dependent volatility model and the application of the spectral methodology where the analytical closed-form pricing formulas for credit-related covenants can be expressed explicitly as infinite series that converge rapidly. We also calibrate our models to market credit default swap (CDS) spreads. Our calibration results show that the non-linear state-dependent volatility model outperforms the geometric Brownian motion (GBM) counterpart.