A closed form solution for pricing defaultable bonds
Résumé
Cathcart and El-Jahel [Journal of Fixed Income 8 (1998)] have formalized the "signaling approach" for modeling the default risk of some risky bonds. Their pricing formula requires a numerical method to invert the Laplace transform of the default probability. This letter rather provides a closed form formula based on standard results of the theory of exotic barrier options. One verifies that the original numerical method implemented by Cathcart and El-Jahel [Journal of Fixed Income 8 (1998)] does not lead to significant computational errors.