Optimal Lending Contract with Uncertainty Shocks

I develop a dynamic agency model of financial contracting, where borrowing constraints appear as part of the optimal contract. The novelty of the paper relative to previous work is that volatility is stochastic and exogenous to the agent behavior. A line of credit appears in the optimal long term contract similar to (DeMarzo and Fishman, 2007). The novelty of the contract is that the credit limit varies over time, as a function of the state of volatility. Credit limit does not vary monotonically over firms. When uncertainty increases, credit limits are reduced for highly constraint firms, because the frictions become harder and the firms lose profitability. Instead, it is optimal to increase the credit limits for less indebted firms, they are still profitable and they need more flexibility to respond to the bigger shocks