Measuring banks' liquidity risk: An option-pricing approach

This paper proposes a new approach to evaluating banks' liquidity needs, which is not only well-grounded theoretically, but is also easy to apply practically. Within the framework of a global game with imperfect information, we first establish a boundary condition for bank runs and show that there exists a unique Nash equilibrium for bank runs. Using the option-pricing approach, we then obtain a closed-form formula for the value of bank equity with both run risk and insolvency risk. Finally, a bank's optimal liquidity ratio is derived by maximizing the value of bank equity. Using data on Chinese listed banks, we show that the deviation of the actual liquidity ratio from the optimal liquidity ratio in a bank represents a robust proxy for its liquidity risk. An increased liquidity shortfall leads to worsening liquidity problems, and this is particularly pronounced when the liquidity shortfall is high. (C) 2019 Elsevier B.V. All rights reserved.