Summary

The option of borrowers to occasionally default on their obligations drives important features of financial markets. In models designed to study such behavior, the discreteness of the default decision induces sizable nonlinearities. Moreover, when debt is long term as in the data, debt dilution is a major force in the determination of borrowing costs: Lenders offer unfavorable prices because all future borrowing and default decisions are salient for the expected payoff of the financial instrument, not only the near-term likelihood of default. Several numerical techniques are employed to compensate for the resulting destabilizing interdependence of borrower policies and asset prices. Among them, approaches based on discrete choice methods have proved particularly tractable and robust. Augmenting otherwise standard sovereign default or unsecured consumer credit models with “taste shocks” to both the borrowing and default choices has been instrumental for their computation and quantitative assessment. These algorithms naturally lend themselves to parallel computation or implementation on Graphics Processing Units and can be readily adapted to richer models incorporating self-fulfilling crises, partial recovery, risk-averse lenders, or multiple endogenous state variables. At the cost of restricting choices to values on a grid, the resulting multinominal logit structure relies on the value functions of the model directly, without taking first-order conditions, costly interpolation, or numerical maximization.