This paper derives formulas for a deposit insuring agency's liability (and hence a fair value deposit insurance premium) and the equilibrium value of bank equity, considering a wide variety of factors affecting individual bank risk. Both fixed rate and variable rate (risk-sensitive) insurance systems are analyzed. Consideration is made as to whether the deposit insuring agency makes direct payments to depositors or arranges mergers following bank closings. The effect of these various policy choices on banks' incentive for risk taking is also analyzed.