A Generalized Endogenous Grid Method for Default Risk Models

The grid search method has often been used to solve models with default risk because the complexity of the problem prevents the use of more efficient but less general tools. In this paper, we propose an extension of the endogenous grid method for default risk models in which price schedules are dependent on individuals' state variables and endogenously determined in equilibrium. Our method combines Fella's (2014) identification for non-concave regions and our algorithm that numerically searches for the risky borrowing limit, a limit that is a theoretical lower bound of the feasible set of asset holdings. The demarcation of this combination enables us to exploit the endogenous grid method by identifying the region of solution sets. The method here is as stable as the grid search method; not only is our method faster and more accurate than the grid search method, but these computational gains are amplified in richer models. With higher accuracy, our method is approximately eight to nine times faster with a simple canonical model of Arellano (2008); approximately 19 to 27 times faster with the richer model of Nakajima and Rıos-Rull (2014). Finally, we show that this method is applicable to a broad class of default risk models by characterizing sufficient conditions for the application. The method may contribute to facilitating the use of model environments with default choices