Optimal Liquidity Control and Systemic Risk in an Interbank Network with Liquidity Shocks and Regime-dependent Interconnectedness

We propose a novel interbank network model in which banks face systemic liquidity shocks, flight-to-quality liquidity flows, and collapses of the interbank network during crises, and study their impacts on the optimal liquidity control and the systemic risk of the interbank network. We find that banks respond to negative shocks by holding positive precautionary liquidity, but once the shock size is sufficiently large, the benefit of precautionary liquidity reduces, and banks lower their precautionary liquidity. Lending (borrowing) banks also hold positive (negative) interbank liquidity provision. Banks hold more provision for more interconnected networks, but when the network is too interconnected, it is too costly to hold large provision, causing banks to lower the provision. On the contrary, a higher degree of the flight-to-quality effect tends to make banks act more aggressively on both precautionary liquidity and interbank provision. As a result, the systemic risk tends to increase in the size of the negative shock, but is quite insensitive to the degree of the flight-to-quality effect. Our analysis shows that the systemic risk increases if the interbank market collapses or becomes too interconnected during crises. Rewards and penalties from regulators can help reduce the systemic risk, but they come with a cost and have different implications on the banks' optimal policies.