We use an exogenous, forward-looking measure of price uncertainty to examine the effect of uncertainty on the use of covenants in private and public debt contracts. The effect of uncertainty differs significantly in loans versus bonds, suggesting that private and public lenders face different incentives when contracting under high uncertainty. In loans, uncertainty increases the use of performance-based covenants. In contrast, covenant usage decreases in bonds, but firms with low agency conflicts mainly drive this effect. However, bondholders require higher spreads to offset the lack of protection with fewer covenants. Hedging does not affect the covenant-uncertainty relationship for debt contracts.

We develop an algorithm for solving a large class of nonlinear high-dimensional continuous-time models in finance. We approximate value and policy functions using deep learning and show that a combination of automatic differentiation and Ito’s lemma allows for the computation of exact expectations, resulting in a negligible computational cost that is independent of the number of state variables. We illustrate the applicability of our method to problems in asset pricing, corporate finance, and portfolio choice and show that the ability to solve high-dimensional problems allows us to derive new economic insights.