This article characterizes the interbank deposit network as a flow network that is able to channel liquidity flows among banks. These flows are beneficial, allowing banks to cope with liquidity risk. First, we analyze the efficiency of three network structures: star-shaped, complete, and incomplete in transferring liquidity among banks. The star-shaped interbank network achieves the complete coverage of liquidity risk with the smallest amount of interbank deposits held by each bank. This result implies that the star-shaped network is most resilient to systemic risk. Second, we analyze the banks’ decentralized interbank deposit decisions for a given network structure. We show that all network structures can generate an inefficiently low amount of interbank deposits. However, the star-shaped network induces banks to hold an amount of interbank deposits that is the closest to the efficient level. These results provide a rationale for consistent empirical evidence on sparse and centralized interbank networks

We develop a simple yet realistic framework to analyze the impact of an exogenous shock on a bank’s balance-sheet and its optimal response when it is constrained to maintain its risk-based capital ratio above a regulatory threshold. We show that in a stress scenario, capital requirements may force the bank to shrink the size of its assets and we exhibit the bank’s optimal strategy as a function of regulatory risk-weights, asset market liquidity, and shock size. When financial markets are perfectly competitive, we show that the bank is always able to restore its capital ratio above the required one. However, for banks constrained to sell their loans at a discount and/or with a positive price impact when selling their marketable assets (large banks) we exhibit situations in which the deleveraging process generates a death spiral. We then show how to calibrate our model using annual reports of banks and study in detail the case of the French bank BNP Paribas. Finally, we suggest how our simple framework can be used to design a systemic capital surcharge