美式多资产期权定价问题的有限差分法  

Finite Difference Method for Pricing Problem of American Multi-asset Option

作　　者：张琪 左平[3] 郝永乐 杨程博[5] 李婷婷 ZHANG Qi;ZUO Ping;HAO Yongle;YANG Chengbo;LI Tingting(School of Science,Shenyang University of Technology,Shenyang 110870,China;Key Laboratory of Symbolic Computation and Knowledge Engineering ofMinistry of Education,Jilin University,Changchun 130012,China;Department of Foundation,Aviation University of Air Force,Changchun 130022,China;School of Mathematics and Statistics,Zhoukou Normal University,Zhoukou 466001,Henan Province,China;College of Mathematics,Jilin University,Changchun 130012,China)

机构地区：[1]沈阳工业大学理学院,沈阳110870 [2]吉林大学符号计算与知识工程教育部重点实验室,长春130012 [3]空军航空大学基础部,长春130022 [4]周口师范学院数学与统计学院,河南周口466001 [5]吉林大学数学学院,长春130012

出　　处：《吉林大学学报（理学版）》2020年第5期1113-1118,共6页Journal of Jilin University:Science Edition

基　　金：国家自然科学基金(批准号:11701210);辽宁省博士启动基金(批准号:20170520014);吉林省优秀青年人才基金项目(批准号:20190103029JH);吉林省自然科学基金学科布局项目(批准号:20200201269JC).

摘　　要：提出一种求解美式多资产期权定价问题的有效算法.首先,利用惩罚法和完全匹配层技巧将多资产期权满足的线性互补模型转化为有界区域上的非线性抛物问题;然后采用半隐式有限差分法求解转化后的非线性问题,并给出该方法的误差结果及数值解的非负性证明;最后利用数值实验验证所提算法的实用性和有效性.We proposed an efficient algorithm for the pricing problem of American multi-asset option.Firstly,by using the penalty method and the perfectly matched layer technique,we transformed the linear complementary model satisfied by multi-asset option into a nonlinear parabolic problem on a bounded domain.Secondly,a semi-implicit finite difference method was used to solve the transformed nonlinear problem,and we gave the error results of the method and the nonnegative proof of the numerical solution.Finally,numerical experiments were used to verify the practicability and effectiveness of the proposed algorithm.

关 键 词：美式多资产期权 半隐式有限差分法 完全匹配层 

分 类 号：O241.8[理学—计算数学]