In this paper we model interbank liquidity networks as fl ow networks. The aim is to compare the ability of different network structures to cope with the liquidity risk faced by the banks. In particular, we analyze the efficiency of three network structures star-shaped, complete and incomplete in transferring liquidity among banks. It turns out that the star-shaped interbank networks achieve the full coverage of liquidity risk with the smallest amount of interbank deposits held by each bank. This means that star-shaped networks generate the minimum counterparty risk for the banks. Moreover, the star-shaped network is more resilient to external shock that can induce contagious defaults. That is, the default of one or more banks is less likely to cause a systemic crisis (i.e., the default of the entire system) in a star-shaped network than in a complete network. These results provides a rationale of the consistent empirical evidence that interbank network are sparse network.
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