永久经理期权的最优实施策略

Optimal Strategies of the Perpetual Executive Stock Options

利用偏微分方程数值方法研究金融市场上永久经理期权(ESOs)的最优实施策略问题.讨论了两种实施情况,即通常的整体实施情况以及非限制实施情况.在非限制实施情况下,持有者在任意可实施时刻可以实施其持有的任意份ESOs.两种实施情况下的最优实施策略分别对应着一个抛物型变分不等式定解问题的自由边界(最佳实施边界).通过数值分析的方法分别研究了自由边界的性质,比较了两种情况下自由边界的异同及其所对应的金融意义.

Using numerical methods of partial differential equations,this paper deals with the optimal exercise strategies of the perpetual executive stock options(ESOs) in financial market.Two exercise situations are discussed,namely,the traditional block exercise and unrestricted exercise.In the case of unrestricted exercise,the holder can exercise any copies of ESOs at any implementation time.The optimal exercise strategies of two exercise situations correspond to the free boundary(the best exercise boundary) of a definite problem about a parabolic variational inequality respectively. The properties of the free boundary are investigated by numerical analysis,and the similarities and differences of the free boundary and the corresponding financial sense in both cases are provided.