华东师范大学学报(自然科学版) ›› 2013, Vol. 2013 ›› Issue (6): 40-45, 56.

• 应用数学与基础数学 • 上一篇    下一篇

美式领子期权定价分析

岑苑君   

  1. 顺德职业技术学院, 广东 佛山 528333
  • 收稿日期:2013-02-01 修回日期:2013-05-01 出版日期:2013-11-25 发布日期:2014-01-13

Pricing model of American collar option

CEN Yuan-jun   

  1. Shunde Polytechnic, Foshan Guangdong 528333, China
  • Received:2013-02-01 Revised:2013-05-01 Online:2013-11-25 Published:2014-01-13

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摘要： 领子期权为持有人设置了保底收益,
也为期权发行方设定了止损上限, 是一种低风险的金融产品.
本文介绍了美式领子期权的数学模型.
它的定价问题是一个退化的抛物型变分不等式,
也是一个障碍非凸的自由边界问题. 通过引入惩罚方法,
运用偏微分方程理论和变分不等式的比较原理分析讨论解的存在唯一性,
以及最佳实施边界的相关性质.

关键词: 美式领子期权, 期权定价, 最佳实施边界

Abstract: Collar option is designed for invertors with a downside
income, and for issuers with a limit loss. The mathematical pricing
model of the American collar option can be formulated as a
one-dimensional parabolic variational inequality, or equivalently, a
free boundary problem. To solve this problem, the penalty method and
PDE arguments are applied. The existence and uniqueness of the
solution, the properties of the free boundaries, such as
monotonicity, smoothness, and location, are presented.

Key words: American collar option, option pricing, optimal exercise boundary

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