经理期权整体实施与非限制实施的等价

THE EQUIVALENCE BETWEEN BLOCK EXERCISE AND UNRESTRICTED EXERCISE OF EXECUTIVE STOCK OPTIONS

经理期权的最优实施策略是计算公司经理期权的发行成本的关键.文章研究了在一定条件下经理期权两种实施策略的等价关系,即整体实施模型与非限制实施模型之间的等价.在先取效用函数再折现的情形下,证明了两种模型的等价性.首先,利用验证定理证明了整体实施下的变分不等式的解就是值函数.接着,证明非限制实施下的变分不等式的解等于整体实施的解.从而证明两种实施模型的等价关系.文章中的效用函数为指数函数,对于其他类型的效用函数,文章的结论和方法仍然有效.特别地,当效用函数为U(y)=y(即不带效用函数)时,两种模型是等价的.

The key of calculating the issuing cost of executive stock options to the firm lies in the optimal exercise strategies of executive stock options. This paper is concerned with the equivalence relation between the two exercise policies of executive stock options under certain conditions, i.e., the equivalence between block exercise model and unrestricted exercise model. The equivalence of the two models is proved in the case of utility function taken prior to discount. First, we prove that the solution of variational inequalities is the value function by use of verification theorem. Then, we prove that the solution of variational inequalities with block exercise is equal to that with unrestricted exercise. And thus the equivalence of the two exercise model is obtained. Although the utility function in the paper is exponential function, the conclusion and method in the paper are still valid for the utility functions of other types. Especially, when the utility function is U（y） = y （i.e., without utility function）, the two models are equivalent.