An analytic derivation of the cost of deposit insurance and loan guarantees An application of modern option pricing theory

Abstract

It is not uncommon in the arrangement of a loan to include as part of the financial package a guarantee of the loan by a third party. Examples are guarantees by a parent company of loans made to its subsidiaries or government guarantees of loans made to private corporations. Also included would be guarantees of bank deposits by the Federal Deposit Insurance Corporation. As with other forms of insurance, the issuing of a guarantee imposes a liability or cost on the guarantor. In this paper, a formula is derived to evaluate this cost. The method used is to demonstrate an isomorphic correspondence between loan guarantees and common stock put options, and then to use the well developed theory of option pricing to derive the formula.