A generalized endogenous grid method for default risk models

Default risk models have been widely employed to assess the ability of households and sovereigns to insure themselves against shocks. Grid search has often been used to solve these models because the complexity of the problem prevents the use of faster but less general methods. In this paper, we propose an extension of the endogenous grid method for default risk models, which is faster and more accurate than grid search. In particular, we find that our solution method leads to a more accurate bond price function, thus making substantial differences in the model's main predictions. When applied to Arellano's (2008) model, our approach predicts a standard deviation of the interest rate spread one-third lower and defaults 3 to 5 times less frequently than does the conventional approach. On top of that, our method is efficient. It is approximately 4 to 7 times faster than grid search when applied to a canonical model of Arellano (2008) and 19 to 27 times faster than grid search when applied to the richer model of Nakajima and Ríos-Rull (2014). Finally, we show that our method is applicable to a broad class of default risk models by characterizing sufficient conditions.