Deposit Insurance with Changing Volatility: An Application of Exotic Options
OFOR Working Paper Number 93-02
Posted: 5 Sep 1994
Merton pioneered the application of the option pricing framework 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 is 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
Suggested Citation: Suggested Citation