A Generalized Endogenous Grid Method for Default Risk Models

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Defaults have been widely observed in financial markets. Researchers use default risk models to better understand the sources of these defaults and the implications of default-related policies. As financial markets and default-related policies have become increasingly complex over time, so have the default risk models.

There are few robust and efficient methods for solving these intricate models. However, despite the increased computational burden and inefficiency, we have relied on the grid-search method for its stability. We propose an extension of the endogenous grid method (EGM), for default risk models. In this method, the debt prices depend on individuals' portfolio positions. We search the regions where EGM can be applied and show how to effectively search the solution in the regions where the EGM cannot be applied. 

Compared with a conventional grid search, our method has similar stability but is faster and more accurate. Specifically, our method is approximately 4 to 7 times faster when applied to a standard model of a sovereign default and approximately 19 to 27 times faster when applied to a richer model. Finally, we show that our method works for a broad class of default risk models.