Managing liquidity: Optimal degree of centralization

Large banking groups face the question of how to optimally allocate and generate liquidity: in a central liquidity hub or in many decentralized branches. We translate this question into a facility location problem under uncertainty. We show that volatility is the key driver behind (de-)centralization. We provide an analytical solution for the 2-branch model and show that a liquidity center can be interpreted as an option on immediate liquidity. Therefore, its value can be interpreted as the price of information, i.e., the price of knowing the exact demand. Furthermore, we derive the threshold above which it is advantageous to open a liquidity center and show that it is a function of the volatility and the characteristic of the bank network. Finally, we discuss the n-branch model for real-world banking groups (10-60 branches) and show that it can be solved with high granularity (100 scenarios) within less than 30 s.