Deposit Insurance with Changing Volatility: An Application of Exotic Options

Abstract

The option pricing framework has been very useful in tackling a wide range of problems. Merton pioneered the application of this methodology to the pricing of deposit insurance for financial institutions. Most applications in the deposit insurance area assume that the volatility of the assets of the bank is exogenous whereas it may be more realistic to assume it is endogenous. We develop a simple model that represents first steps in this direction. It is assumed that the volatility of the bank's assets changes or can be changed when the assets first hit a certain level. We permit the volatility to be selected in an optimal fashion at this barrier and develop expressions for the shareholders' equity and the deposit insurance premium. This analysis uses generalizations of particular types of barrier options known as down-and-out and down-and- in options. Numerical examples are developed to illustrate the properties of the model.

JEL Classification: G13, G21, G28