A Generalized Endogenous Grid Method for Models with the Option to Default

We develop an endogenous grid method for models with the option to default in which price schedules are endogenously determined in equilibrium and depend on individuals’ states. The algorithm has noticeable computational benefits in efficiency and accuracy. We obtain these computational benefits by combining Fella’s (2014) identification for non-concave regions with our algorithm that numerically searches for risky borrowing limits. These two procedures identify the region of solution sets to which Carroll’s (2006) endogenous grid method is applicable. To demonstrate the method, we apply our method to Nakajima and Rios-Rull’s(2014) model. In terms of computation time, this method is seven to twenty-seven times faster than the conventional grid search method. Moreover, various types of accuracy tests indicate that our method yields more accurate results than the grid search method.