Draft with with Sean McCrary, José-Víctor Ríos-Rull and Adrien Wicht, June 2024
Abstract: We characterize the equilibrium of the standard sovereign default model where a risk-averse borrower issues long-term non-contingent bonds but cannot commit its future selves to repay. We show existence of the Markov equilibrium and and uniqueness of equilibria that are the limit of finite economies. We show that the price and policy functions exhibit jumps and kinks in various places. A suitable choice of arbitrary small noise yields price and policy functions that are differentiable almost everywhere which allows us to characterize the equilibrium using only decision rules of the agents by means of a set of functional equations. Further, we describe the equilibrium objects via an Euler equation with derivatives on future actions—i.e. a generalized Euler equation (GEE) where the effects due to default and those to dilution can be disentangled. These functional equations allow for computational strategies that search for continuous policy functions and provide criteria to verify that the objects found are indeed equilibria. A sufficient variance of the noise allows for concavity and hence unique solution of the GEE.
Older version with Jose-Victor Rios-Rull
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.
In progress. Some old slides download