Pricing model of American collar option
-
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.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
-
[1] {1} 雍炯敏, 刘道百. 数学金融学[M]. 上海: 上海人民出版社, 2003.{2} 蒲冰远, 唐应辉, 袁勋. 连续支付红利及有交易成本的领子期权定价模型[J]. 数学的实践与认识, 2009, 39: 37-41.{3} JIANG L S. Mathematical Modeling and Methods of Option Pricing[M]. Singapore: World Scientific, 2005.{4} FRIEDMAN A. Variational Principle and Free Boundary Problems[M]. [s.l]: John Wiley $\&$ Sons, 1982.{5} GUO X, SHEPP L. Some optimal stopping problems with nontrival boundaries for pricing exotic options[J]. Journal of Applied Probability, 2001, 38: 647-658.{6} 易法槐, 余涛. 源于俄式期权定价的自由边界问题[J]. 应用数学学报, 2008, 31: 993-1012.
点击查看大图
计量
- 文章访问数: 1528
- HTML全文浏览量: 16
- PDF下载量: 1432
- 被引次数: 0