A Theory of Bank Illiquidity and Default with Hidden Trades

How does the availability of alternative investment opportunities for banks' depositors affect the reaction of the banking system to aggregate liquidity shocks? And what are the implications, if any, for banking regulation? To answer these questions, I study a Diamond-Dybvig environment, where banks hedge against aggregate liquidity risk in the interbank market or default, and depositors borrow and lend in a hidden-bond market. In this framework, banks offer an endogenously incomplete contract, and default in equilibrium only when facing systemic liquidity risk. In this case, the allocation at default is inefficient, and countercyclical liquidity requirements are welfare-improving.