A parabolic variational inequality arising from the valuation of strike reset options

作者：Yang Zhou; Yi Fahuai^*; Dai Min

来源：Journal of Differential Equations, 2006, 230(2): 481-501.

DOI：10.1016/j.jde.2006.07.026

• option pricing
• strike reset option
• free boundary
• variational inequality
• American option

A strike reset option is an option that allows its holder to reset the strike price to the prevailing underlying asset price at a moment chosen by the holder. The pricing model of the option can be formulated as a one-dimensional parabolic variational inequality, or equivalently, a free boundary problem, where the free boundary just corresponds to the optimal reset strategy adopted by the holder of the option. This paper is concerned with the theoretical analysis of the model. The existence and uniqueness of the solution are established. Furthermore, we study properties of the free boundary. The monotonicity and C(infinity) smoothness of the free boundary are proven in some situations.

• 出版日期2006-11-15
• 单位北京大学