具有不连续两级上限的美式期权
American Options with Discontinuous Two-Level Caps
摘要：
本文研究了具有两个上限的美式封顶看涨期权的定价问题。直接行使区域的结构是显着更复杂的比在经典的情况下，常数帽。当上限随着时间的推移而增长时，我们广泛使用概率参数和当地时间，证明了练习区域可以是两个不连通集的并。或者，它可以由两组由一条线连接。问题，然后减少到第一组，这是满足递归积分方程的上边界的表征。当上限随时间减小时，锻炼区域的边界具有与非增加段交替的分段恒定段。推导了包含执行边界和标的价格过程局部时间的期权价格的一般表示公式。一个有效的算法开发和数值结果提供。
英文摘要：
This paper examines the valuation of American capped call options with two-level caps. The structure of the immediate exercise region is significantly more complex than in the classical case with constant cap. When the cap grows over time, making extensive use of probabilistic arguments and local time, we show that the exercise region can be the union of two disconnected set. Alternatively, it can consist of two sets connected by a line. The problem then reduces to the characterization of the upper boundary of the first set, which is shown to satisfy a recursive integral equation. When the cap decreases over time, the boundary of the exercise region has piecewise constant segments alternating with non-increasing segments. General representation formulas for the option price, involving the exercise boundaries and the local time of the underlying price process, are derived. An efficient algorithm is developed and numerical results are provided.
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