英文标题：
《American Options with Discontinuous Two-Level Caps》
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作者：
Jerome Detemple and Yerkin Kitapbayev
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最新提交年份：
2017
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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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中文摘要：
本文研究了具有两级上限的美式有上限看涨期权的估值问题。即时运动区的结构明显比具有恒定cap的经典情况更复杂。当cap随时间增长时，通过广泛使用概率参数和局部时间，我们证明了运动区域可以是两个断开集的并集。或者，它可以由两组由一条线连接的装置组成。然后，该问题归结为第一个集合的上边界的特征，它被证明满足一个递归积分方程。当cap随时间减少时，运动区域的边界具有分段恒定段，与非增加段交替。推导了期权价格的一般表示公式，包括行权边界和标的价格过程的本地时间。提出了一种有效的算法，并给出了数值结果。
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分类信息：

一级分类：Quantitative Finance 数量金融学
二级分类：Pricing of Securities 证券定价
分类描述：Valuation and hedging of financial securities, their derivatives, and structured products
金融证券及其衍生产品和结构化产品的估值和套期保值
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