Deposit insurance and forbearance under moral hazard

We study the efficacy of forbearance using a real options approach. Our model endogenizes moral hazard embedded in credit risk undertaken by the bank. The bank's interest rate risk is modeled as duration mismatch. Other modeling improvements over previous studies include such features as stochastic interest rates and deposits, continuous interest payments on an ongoing deposit portfolio, and a stochastic forbearance period. We find that the bank does have an incentive to engage in undue risk taking. Even in the presence of moral hazard, however, forbearance can still be a desirable course of action in reducing the FDIC's expected liability. In addition, the capital ratio plays an extremely important role in determining the fair insurance premium. Finally, using the mismatch of asset and deposit durations as the correct measurement of interest rate risk, our model reveals that an optimal asset variance may exist for a particular bank, contrary to what the contingent claims framework would predict. Therefore, we resolve the puzzle that banks in practice do not increase asset risk to take full advantage of the limited liability.