Pricing mutual bank deposit guarantees

The pricing of bank deposit insurance is the starting point in understanding how the design of a depositors' protection system can impact on the risk taking attitude of banks and on the social costs incurred in implementing such a system. In any case a crucial role is played by the regulator who has the task to implement actions aimed to manage the cost-benefits trade-off related to the deposit insurance mechanism. In our paper we price the guarantee's value within a mutual deposit insurance system similar to the one adopted in Italy and many other European countries. The main feature of such a guarantee scheme is that of directly involving banks into the insuring process through the participation to an interbank fund which concurs with the Government in covering losses to depositors of failed banks. We show that the guarantee's value corresponds to the value of a portfolio of three non-standard European options written on multiple underlyings (i.e. all the assets of insured banks). The complexity of such derivatives doesn't allow to find a closed form solution to the pricing problem. Monte Carlo techniques are implemented in order to value the three options in the portfolio. Our analysis evidences an adverse incentive of insured banks to undertake as much risk as possible. We show how introducing a lower barrier (Parisian style) into the synthetic option positions (i.e. a minimum value of the coverage ratio) below which the bank is excluded by the guarantee system after an assigned time interval, mitigates substantially the aforementioned adverse incentive affecting banks' behavior. Furthermore, a contingent ex-post benefit paid to the bank conditional on its presence into the insuring mechanism, turns out to be effective in controlling the risk undertaking of credit institutions.