An Optimal Strategy for Liquidity Management in Banking

During the global financial crisis, banks were under severe pressure to maintain adequate liquidity. This resulted in demands for cash from various sources, including counterparties, short-term creditors, and, especially, existing borrowers. Also, banks were forced to maintain more liquid assets in the event of unexpected future losses that may occur from securities write-downs. This can cause a detrimental effect on its investment portfolio and lending activities. In response to the liquidity crises the Basel Committee on Banking Supervision (BCBS) designed a set of precautionary measures (known as Basel III) imposed on banks and one of its purposes is to protect the economy from deteriorating. Recently, bank regulators wanted banks to depend on sources such as core deposits and long-term funding from small businesses and less on short-term wholesale funding. This was an attempt to protect banks from being vulnerable to another financial crises. In order to address the aforementioned problem, we investigate the money supply process between a central bank and a commercial bank and how it influences the liquidity of a bank. In particular, we formulate a stochastic control problem involving cash which is held as deposits at a central bank. The solution of this problem is readily obtained from existing literature. Using simulations we investigate the manner in which this interplay affects the liquidity coverage ratio of a bank. Finally, we make a few concluding remarks and discuss possibilities for further research. We acknowledge financial support by the National Research Foundation of South Africa. Corresponding author 276 Garth J. van Schalkwyk and Peter J. Witbooi