[1]岑苑君,易法槐.适于风险厌恶型投资的美式看涨期权定价分析[J].南京师范大学学报(自然科学版),2015,38(04):71.
 Cen Yuanjun,Yi Fahuai.An American Call Option Pricing Model for Risk-Averse Invertors[J].Journal of Nanjing Normal University(Natural Science Edition),2015,38(04):71.
点击复制

适于风险厌恶型投资的美式看涨期权定价分析()
分享到:

《南京师范大学学报》(自然科学版)[ISSN:1001-4616/CN:32-1239/N]

卷:
第38卷
期数:
2015年04期
页码:
71
栏目:
数学
出版日期:
2015-12-30

文章信息/Info

Title:
An American Call Option Pricing Model for Risk-Averse Invertors
作者:
岑苑君1易法槐2
(1.顺德职业技术学院高职数学教研室,广东 佛山 528333)(2.华南师范大学数学科学学院,广东 广州 510631)
Author(s):
Cen Yuanjun1Yi Fahuai2
(1.Section of Higher Vocational Mathematics,Shunde Polytechnic,Foshan 528333,China)(2.School of Mathematics,South China Normal University,Guangzhou 510631,China)
关键词:
美式看涨期权期权定价最佳实施边界
Keywords:
the standard American optionsoption pricingoptimal exercise boundary
分类号:
O175.26
文献标志码:
A
摘要:
介绍了为风险厌恶型投资者所设计的新型美式看涨期权的数学模型.它的定价问题是一个退化的抛物型变分不等式,也是一个自由边界(即最佳实施边界)问题.与标准美式看涨期权不同,这种新型期权在股票分红时有两条光滑单调的自由边界,而当股票不分红时仅有一条直线型的自由边界.本文运用偏微分方程方法分析讨论解的存在唯一性,自由边界的单调性、连续性、可微性以及关于事先承诺的价格[l]的相关性质.
Abstract:
There is a new American call option which is designed for risk-averse invertors. The mathematical pricing model of this option can be formulated as a one-dimensional parabolic variational inequality,or equivalently,a free boundary problem. Different from the standard American call,it has two monotonous smooth free boundaries with dividends and has only one linear free boundary without dividends. To solve this problem,PDE arguments are applied. We can prove the existence and uniqueness of the solution. Then the properties of the free boundaries,such as monotonicity,smoothness,and location,are presented.

参考文献/References:

[1]BLANK F,SCHOLES M. The pricing of options and corporate liabilities[J]. Political economy,1973,81(3):637-654.
[2]WILMOTT P,DEWYNNE J,HOWISON S. Option pricing[M]. London:Oxford Financial Press,1993.
[3]GUO X,SHEPP L. Some optimal stopping problems with nontrival boundaries for pricing exotic options[J]. Appl Prob,2001,38:647-658.
[4]JIANG L S. Mathematical modeling and methods of option pricing[M]. Singapore:World Scientific,2005.
[5]AVNER FRIEDMAN. Variational principle and free boundary problems[M]. New York:John Wiley & Sons,1982.
[6]陈亚浙. 二阶抛物型偏微分方程[M]. 北京:北京大学出版社,2003.
[7]CONNON J R,HENRY D B,KOTLOV D B. Continuous differentiability of the free boundary for weak solutions of the Stefan problem[J]. Bull Ane Math Soc,1974,80:45-48.
[8]FRIEDMAN A. Parabolic variational inequalities in one space dimension and smoothness of the free boundary[J]. J?Funct Anal,1975,18:151-176.

相似文献/References:

[1]刘睿辰,刘国祥,叶 伟.一类跳扩散过程下期权定价公式的参数估计[J].南京师范大学学报(自然科学版),2014,37(03):36.
 Liu Ruichen,Liu Guoxiang,Ye Wei.Parameter Estimation of the Option Pricing Formula ona Class of Jump-Diffusion Model[J].Journal of Nanjing Normal University(Natural Science Edition),2014,37(04):36.

备注/Memo

备注/Memo:
收稿日期:2014-12-23.
基金项目:国家自然科学基金(11271143、11371155)、顺德职业技术学院校级科研项目(2015-KJZX017)、高等学校博士学科点专项科研基金(20124407110001).
通讯联系人:岑苑君,讲师,研究方向:金融数学. E-mail:yuanjuncen@163.com
更新日期/Last Update: 2015-12-30