Perpetual American Put Option With Default Risk

摘要

An American option gives the owner the right to buy or sell an underlying asset at a specified strike price on any trading day or before expiration. It has become an important financial derivative, and plays an essential role in the financial market. In this paper, we introduce the credit risk to enhance practicability of the option. Once credit risk occurs, the option will lapse immediately. In the context of a reduced form model driven by a Brownian motion, we give the explicit solution to the American put option based on the constant default intensity function, and the solutions of free boundary problems are also obtained. It turns out that the structure of optimal stopping strategies has changed since the credit risk is taken into account.