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求解美式回望期权的有限元方法

本站小编 Free考研考试/2021-12-27

宋海明1, 张琪1, 李景治2, 刘宏宇3
1. 吉林大学数学学院, 长春 130012;
2. 南方科技大学数学系, 广东深圳 518055;
3. 香港浸会大学数学系, 香港
收稿日期:2015-11-02出版日期:2016-08-15发布日期:2016-09-08
通讯作者:李景治,Email:li.jz@sustc.edu.cn.

基金资助:国家自然科学基金(11271157,11371171,11201453,11571161)资助项目,深圳市科创委基础研究基金(JCYJ20140509143748226)资助项目.


FINITE ELEMENT METHOD FOR VALUATION OF AMERICAN LOOKBACK OPTIONS

Song Haiming1, Zhang Qi1, Li Jingzhi2, Liu Hongyu3
1. Department of Mathematics, Jilin University, Changchun 130012, China;
2. Department of Mathematics, South University of Science and Technology of China, Shenzhen 518055, Guangdong, China;
3. Department of Mathematics, Hong Kong Baptist University, Hong Kong SAR, China
Received:2015-11-02Online:2016-08-15Published:2016-09-08







摘要



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期权作为一种金融衍生产品,在欧美国家一直很受欢迎.由于其规避风险的特性,期权也吸引了中国投资者的兴趣.%基于市场的需求,2015年初,上海证券交易所推出了中国首批期权产品,期权定价问题的研究热潮正席卷全球.本文研究的美式回望期权,是一种路径相关的期权,其支付函数不仅依赖于标的资产的现值,也依赖其历史最值.分析回望期权的特点,不难发现:1)这类期权空间变量的变化范围为二维无界不规则区域,难以应用数值方法直接求解;2)最佳实施边界未知,使得该问题变得高度非线性.本文的主要工作就是解决这两个困难,得到回望期权和最佳实施边界的数值逼近结果.现有的处理问题1)的有效方法是采用标准变量替换、计价单位变换以及Landau变换将定价模型化为一个[0,1]区间上的非线性抛物问题,本文也将沿用这些技巧处理问题1).进一步,采用有限元方法离散简化后的定价模型,并论证了数值解的非负性,提出了利用Newton法求解离散化的非线性系统.最后,通过数值模拟,验证了本文所提算法的高效性和准确性.
MR(2010)主题分类:
65N30
65M60

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