Optimal Bank Interest Margin with Synergy Banking under Capital Regulation and Deposit Insurance: A Swaption Approach

The main purpose of this paper is to model bank spread behavior under capital regulation and deposit insurance. Comparative static results show that an increase in the capital-to-deposits ratio or the deposit insurance decreases the bank's interest margin or spread. It is also shown that an increase in the equity that implies its opportunity cost of the coupon rate on the fixed leg decreases the margin. Previous research on market-based evaluations of bank equity has modeled the bank as a narrowing banking firm with risky assets and insured liabilities. The equity of the bank is viewed as a call option on its risky assets. No attempt was made to explicitly analyze a synergy between lending and deposit-taking, and, in our view, the equity of the bank is viewed as a swap option on coupon bonds. Synergy banking, particularly in the return to retail banking, is important in distinguishing banks from other lenders such as finance companies and mutual fund institutions. These other lenders call for the breaking up of banks into separate lending and deposit-taking operations, respectively. Our findings provide an insight for synergy banking operations concerning regulated bank spread behavior in the return to retail banking.