The Value of Deposit Insurance in the Presence of Interest Rate and Credit Risk

In this paper we employ the theory of the term structure of interest rates and the pricing of interest contingent contracts to determine the fair value of insurance for depository institutions. The balance sheet of a bank is taken to consist of long and short positions in various fixed income securities. Deposit insurance for the bank is a put option on the value of the assets. The value of deposits, assets, the implied exercise price of the put and the value of the put are all determined simultaneously as part of the same valuation solution. The approach is developed initially for a single-state term structure. It is extended to incorporate credit risk on bank assets. The most important policy implication is that for a bank whose assets are longer term than its liabilities and whose borrowers are not excessively leveraged the properly calculated, risk-adjusted deposit insurance premia are increasing functions of the level of interest rates. Sensitivity analyses also treat such factors as the bank’s deposit to asset ratio, duration gap, interest volatility, the volatility of assets backing the bank loans, and the bank’s borrowers’ debt to equity ratio.