Exercise Boundary Near Maturity for an American Option on Several Assets

Abstract

We consider an American put option on a linear function of d dividend-paying assets. The value function of this option is given as the solution of a free boundary problem. When d = 1, the behavior of the free boundary near the maturity of the option is well known. In this article, we extend to the case d > 1 the study of the free boundary near maturity. A parameterization of the stopping region at time t is given. That enables us to define and give a convergence rate for this region when t goes to the maturity.

Keywords:

• American options
• Free boundary
• Optimal stopping
• Variational inequality

Mathematics Subject Classification:

• 91B24
• 60G40
• 93E20