Pricing American put options on defaultable bonds

In the last two decades, the market of credit derivatives has expanded rapidly, and the importance of pricing problems for credit derivatives has been recognized especially in the last decade. Among these securities, the pricing problems of credit derivatives with an early exercise, such as American put options, have not received enough attention. In view of this need, this paper develops a continuous stochastic model of American put options on defaultable bonds. The method of obtaining a solution is based on a new result of the optimal stopping problem for a diffusion process with a jump. Some characterizations of American put options are provided using partial differential equations.