This paper presents a framework where many existing structural credit risk models can be made hybrid by using a transformation of leverage to define the default intensity. The approach supports stochastic interest rates as well. As the default trigger is not purely specified by an exogenous barrier, the model produces endogenous random recovery rates that are negatively correlated to the default probabilities, which is consistent with the empirical findings. The key contributions of the paper are as follows. First, default intensity is defined as an increasing and convex transformation of leverage. Second, the recovery rate model uses leverage at default in a cascade manner to account for different debtholders seniority. Third, the approach is implemented on a firm-by-firm basis using maximum likelihood and the unscented Kalman filter (UKF). This accounts for trading noises which are deviations from theoretical prices. Finally, the non-linearity between default intensity and leverage is investigated empirically on each company of the CDX NA IG and HY indices using monthly CDS data from January 2004 to May 2008.