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This paper aims to develop a barrier cap option model, i.e. a cap option model where default can occur at any time before the maturity date, to evaluate the equity and the default risk of a bank. The model implies the bank as a liquidity provider that one institution carriers out both lending and deposit-taking functions under the same roof. This paper studies the impacts of demand deposits and capital regulation on the optimal bank interest margin, i.e. the spread between the loan rate and the deposit rate.

This paper characterizes the bank’s equity value by a barrier cap option framework. In the model, default can occur at any time before the maturity and loan markets are imperfectly competitive.

This paper has two main results. First, increases in demand deposits reduce the bank’s interest margin and further increase the bank’s default risk. The negative effect on the optimal bank interest margin which ignores the barrier leads to significant overestimation; the positive effect on the default risk which ignores the barrier leads to underestimation. Second, the same pattern of capital regulation as previously applies. Capital regulation as such makes the bank more prone to loan risk-taking, thereby adversely affecting the stability of banking system.

This paper reintroduces the knock-out value and bank interest margin determination within a synergy banking function to the cap option model. The results confirm the need to model bank equity as a barrier cap option and demonstrate its usefulness in capital regulation.