Optimal Centralization of Liquidity Management

Abstract

Liquidity is a key resource that banks have to manage on a daily basis. Large banking groups face the question of how to optimally allocate and generate liquidity: in a central liquidity hub or in many decentralized branches across different time zones, jurisdictions, and FX zones. We rephrase the question as a facility-location problem under uncertainty. We show that volatility is a key driver of the degree of (de-)centralization. As expected, in a deterministic setup liquidity should be managed centrally in the most profitable branch. However, under stochastic liquidity demand and different time zones, FX zones, and jurisdictions we find that liquidity is preferably managed and generated in a decentralized fashion to a certain extend. We provide an analytical solution for the 2-branch model. In our setup, a liquidity center is an option on immediate liquidity. Therefore, its value can be interpreted as the “price of information”, i.e. the price of knowing the demand. Furthermore, we derive the threshold 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 (n = 10 to 60 branches) and show that it can be solved with high granularity (100 scenarios) within less than 30 seconds.