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# G21 – Banks; Depository Institutions

To capture the benefits of banking activity and liquidity provision, we assume that each dollar of safe short-term debt issued by the bank yields a liquidity benefit |$\gamma >0$| over and above the cash flows backing this claim. This assumption captures, in reduced form, the benefits from maturity transformation performed by banks4 and the nonpecuniary liquidity services obtained from safe money-like securities issued by banks.5

Banking operations yield cash flows at dates |$1$| and |$2$|⁠. Two aggregate states are possible at date |$1$|⁠. With probability |$p_{1}$|⁠, the high aggregate state occurs, and both operating subsidiaries receive a high cash flow |$C_{1}^{H}$|⁠. With probability |$1-p_{1}$|⁠, the low aggregate state is realized, and both subsidiaries receive the low cash flow |$0<C_{1}^{L}<C_{1}^{H}$|⁠. The aggregate state captures undiversifiable cash-flow risk that both operating subsidiaries are exposed to. For simplicity, we assume that the two operating subsidiaries have the same exposure to the aggregate shock.

In addition to this aggregate cash-flow risk, the operating subsidiaries are also exposed to diversifiable cash-flow risk at date |$1$|⁠. Specifically, we assume that one of the two banking subsidiaries receives an additional cash flow of |$\Delta >0$|⁠. This additional cash flow |$\Delta$| is received by the operating subsidiary in jurisdiction |$i$| with probability |$\theta _{i}$|⁠, where |$\theta _{1}+\theta _{2}=1$|⁠. Therefore, even though |$\Delta$| is risk-free from a global perspective, it is a risky cash flow from the perspective of each individual operating subsidiary.6 We assume that the bank cannot easily hedge this risk.7 We assume that |$C_{1}^{H}$| is sufficiently high that both operating subsidiaries can meet their short-term liabilities in the high cash-flow state, regardless of who receives |$\Delta$|⁠. When |$C_{1}^{L}$| is realized, on the other hand, the banking subsidiaries will not necessarily have sufficient funds to repay or roll over their short-term debt obligation |$R_{1}$|⁠, thereby creating a need for bank resolution.