A free boundary problem arising from pricing convertible bond

Abstract

In this article we study the behaviours of the optimal conversion boundary (i.e. free boundary) of an American-style convertible bond with finite horizon (i.e. parabolic case). We prove the existence and the uniqueness of the strong solution of the problem and the boundedness and smoothness of the free boundary. Moreover, we characterize the free boundary's start point and present two numerical results.

Keywords:

• convertible bond
• American-style
• free boundary
• variational inequality

AMS Subject Classifications:

• 35R35
• 91B28

Acknowledgements

The project is supported by NNSF of China (No. 10971073, No. 10801056 and No. 10901060) and NNSF of GuangDong province (No. 9451063101002091).