A Direct Solution Method for Pricing Options involving the Maximum Process
A Direct Solution Method for Pricing Options involving the Maximum Process
复制标题
涉及最大过程的定价期权的直解法
DOI：
10.1007/s00780-017-0343-5
复制
发表时间：
2017
影响因子：
1.7
通讯作者：
M. Egami and T. Oryu
中科院分区：
文献类型：
--
作者：
Shibata;T.;Libby Chan;M. Egami and T. Oryu
人们经常会遇到不仅涉及股价，而且还涉及其运行最高值的期权。在相当一般的情况下，我们给出了与扩散过程及其运行极大值有关的最优停止问题的显式解。我们的方法是使用马尔可夫过程的游程理论，将原始的二维问题重写为无穷多个一维问题。我们的方法是相当直接的，没有预先假定最优阈值的存在，也没有强加平滑拟合条件。通过经典算例和新算例，给出了一种系统的求解方法。
One often encounters options involving not only the stock price, but also its running maximum. We provide, in a fairly general setting, explicit solutions for optimal stopping problems concerned with a diffusion process and its running maximum. Our approach is to use excursion theory for Markov processes and rewrite the original two-dimensional problem as an infinite number of one-dimensional ones. Our method is rather direct without presupposing the existence of an optimal threshold or imposing a smooth-fit condition. We present a systematic solution method by illustrating it through classical and new examples.