A Barrier Option Utility Framework for Bank Interest Margin under Government Bailout

The barrier options theory of corporate security valuation is applied to the contingent claims of a distressed bank under a bailout program of distressed loan purchases. In particular, the bank acts as if it has a single utility function that positively weights equity returns like, but negatively weights bankruptcy dislike. We show that an increase in the amount of distressed loan purchases decreases the loan amount at an increased margin when buying distressed loan amount is high. Bailout as such makes the bank less prone to loan risk taking, thereby contributing the stability of the banking system. A numerical exercise shows that the market-based estimates of the expected utility of bank equity returns which ignore the weights (a standard down-and-out call option) or the dislike (a standard call option) lead to significant overestimation.