Formation of Optimal Interbank Lending Networks under Liquidity Shocks
Daniel E. Rigobon, Ronnie Sircar
We formulate a model of the banking system in which banks control both their
supply of liquidity, through cash holdings, and their exposures to risky
interbank loans. The value of interbank loans jumps when banks suffer liquidity
shortages, which can be caused by the arrival of large enough liquidity shocks.
In two distinct settings, we compute the unique optimal allocations of capital.
In the first, banks seek only to maximize their own utility -- in a
decentralized manner. Second, a central planner aims to maximize the sum of all
banks' utilities. Both of the resulting financial networks exhibit a
`core-periphery' structure. However, the optimal allocations differ --
decentralized banks are more susceptible to liquidity shortages, while the
planner ensures that banks with more debt hold greater liquidity. We
characterize the behavior of the planner's optimal allocation as the size of
the system grows. Surprisingly, the `price of anarchy' is of constant order.
Finally, we derive capitalization requirements that cause the decentralized
system to achieve the planner's level of risk. In doing so, we find that
systemically important banks must face the greatest losses when they suffer
liquidity crises -- ensuring that they are incentivized to avoid such crises.