模系矩阵分裂迭代法定价机制转换下的美式Kou型跳扩散期权  

Modulus-Based Matrix Splitting Iteration Methods Pricing American Options under Regime-Switching Kou's Jump-Diffusion

作　　者：李永杰 刘雯娜 刘健 黄勤友 甘小艇[1] LI Yongjie;LIU Wenna;LIU jian;HUANG Qinyou;GAN Xiaoting(School of Mathematics and Computer Science,Chuxiong Normal University,Chuxiong Yunnan 675o00,China)

机构地区：[1]楚雄师范学院数学与计算机科学学院,云南楚雄675000

出　　处：《重庆师范大学学报（自然科学版）》2023年第2期119-125,共7页Journal of Chongqing Normal University:Natural Science

基　　金：国家自然科学基金面上项目(No.61463002);中央高校基本科研业务费专项资金项目(No.22120210555);云南省地方本科高校联合专项面上项目(No.2019FH001-079);云南省大学生创新训练项目(No.202111391079)。

摘　　要：[目的]研究机制转换下的美式Kou型跳扩散期权模型的数值解法。[方法]基于Crank-Nicolson拟合有限体积法离散得到的线性互补问题,引入高效的模系矩阵分裂迭代法进行求解。[结果]给出了H+离散矩阵下算法的收敛性定理。[结论]数值实验验证了新方法的有效性、稳健性和收敛性,且模系矩阵分裂迭代法的计算效率优于投影超松弛迭代法。[Purposes]As for the valuation of American options under regime-switching Kou's jump-diffusion processes.[Methods]Based on the linear complementarity problem discretized by Crank Nicolson fitted finite volume method,an efficient modulus matrix splitting iterative method is introduced to solve it.[Findings]The convergence theorem of the algorithms are given under the H^(+)-matrix property of the discrete matrix.[Conclusions]Numerical experiments verify the effectiveness,robustness and convergence of the new method,and the computational efficiency of themodulus-based matrix splitting iteration methods is superior to the projected successive overrelaxation iteration method.

关 键 词：机制转换下的美式Kou型跳扩散期权 线性互补问题 模系矩阵分裂迭代法 

分 类 号：O241.82[理学—计算数学]