On the Cost of Deposit Insurance When There Are Surveillance Costs

In an earlier paper on the cost of deposit insurance and loan guarantees (Merton 1977a), I demonstrated an isomorphic correspondence between loan guarantees and common stock put options. Using this correspondence and the well-developed theory of option pricing, a formula was derived to evaluate these liabilities. If the guarantor chooses to audit only at the end of a finite, specified period, then the same analysis applies to the evaluation of demand-deposit guarantees. While the reason given for the finite time between audits was the cost to the guarantor of continuous surveillance, no explicit recognition of these costs was presented in the model. Although based on the same structure, the model developed in this paper extends the earlier development to take into account explicitly surveillance or auditing costs and to provide for random auditing times. Under the assumption of free entry into the banking industry, the equilibrium interest rate on deposits is derived. Further, it is shown that, in effect, depositors pay for the surveillance costs and the equity holders of the bank pay for the put option component of the deposit guarantee. A model for evaluating the cost of deposit insurance is derived that explicitly takes into account surveillance or auditing costs and provides for random auditing times. The method used to derive this evaluation formula exploits the isomorphic correspondence between loan guarantees and common stock put options. Because of these auditing costs, the equilibrium rate of return on deposits will be below the market interest rate even in a competitive banking industry with no transactions costs. Further, it is shown that the auditing cost component of the deposit insurance premium is, in effect, paid for by the depositors, and the put option component is paid for by the equity holders of the bank. * I thank Fischer Black for many helpful discussions. This paper was presented at the Joint Stanford-Berkeley Seminar in Finance, February 1977. I thank the participants for their comments. Aid from the National Science Foundation is gratefully acknowledged.