Systemic risk, interbank relations and liquidity provision by the Central Bank

We model systemic risk in an interbank market. Banks face liquidityneeds as consumers are uncertain about where they need to consume. Interbank credit lines allow to cope with these liquidity shocks while reducing the cost of maintaining reserves. However, the interbank market exposes the system to a coordination failure(gridlock equilibrium) even if all banks are solvent. When one bankis insolvent, the stability of the banking system is affected in various ways depending on the patterns of payments across locations. We investigate the ability of the banking industry to withstand the insolvency of one bank and whether the closure ofone bank generates a chain reaction on the rest of the system. Weanalyze the coordinating role of the Central Bank in preventing payments systemic repercussions and we examine the justification ofthe Too-big-to-fail-policy.