with Sean McCrary, José-Víctor Ríos-Rull and Adrien Wicht, June 2026
Abstract: We characterize the equilibrium of the standard sovereign default model with long-term, non-contingent debt. We show existence of the Markov equilibrium and uniqueness of equilibria that are the limit of finite economies. In general, the price and policy functions exhibit jumps and kinks; a suitable choice of arbitrarily small noise yields price and policy functions that are differentiable almost everywhere, which allows us to characterize the equilibrium using only the agents’ decision rules by means of a set of functional equations. We further describe the equilibrium objects via an Euler equation with derivatives on future actions—a Generalized Euler Equation (GEE) in which the effects due to default and those due to dilution can be disentangled. The GEE yields computational strategies that search for continuous policy functions. A sufficient scale of the noise ensures concavity and a unique solution of the GEE. Applied to a calibrated model following Chatterjee and Eyigungor (2012), the GEE combined with the endogenous grid method delivers residuals orders of magnitude smaller than standard value function iteration, at roughly an order of magnitude lower computational cost.
with Jose-Victor Rios-Rull, older version 2016
Abstract: We show how to characterize the Markov equilibrium of the class of problems of unilateral default by means of functional equations including a Generalized Euler Equation, that is, an Euler equation that includes derivatives of decision rules as its arguments. The functional equations gives insights into the different margins: marginal utilities today and tomorrow, increased probabaility of future default and dilution of future debt with associated debt prices changes. A comparison with the functional equations that result from the problem under commitment provides additional insights into these environments without commitment. Our approach inspires the use of computational methods that take advantage of the derivatives of the decision rules for controlled accuracy even in the presence of kinks.