Strategic bank closure and deposit insurance valuation

Abstract

This study formulates the deposit insurance valuation problem as a zero-sum optimal stopping game using Israeli option with bankruptcy cost. Specifically, closure of a bank is framed as a game between the insured bank and the deposit insurer, in which a bank with financial difficulties is choosing an optimal self-closure point to maximize its benefits from the deposit insurance scheme; and the deposit insurer is choosing an optimal regulatory closure point to minimize their cost of offering the insurance. In such setting, the deposit insurance itself could be regarded as an Israeli put option. With bankruptcy costs taken into consideration, we managed to derive the closed-form solutions to the deposit insurance premium together with the endogenous closure points. Our model could also be used to justify the scenarios of too big to fail, reorganization of problematic bank, and regulator’s forbearance.