定价Kou跳扩散美式期权模型的一种有效算法  

An Efficient Algorithm for Pricing American Option Under Kou Jump Diffusion Model

作　　者：豆铨煜 王励冰 刘梅 DOU Quan-yu;WANG Li-bing;LIU Mei(School of Mathematics and Information Science,Zhengzhou University of Light Industry,Zhengzhou 450002,China;School of Mathematics and Statistics,Zhoukou Normal University,Zhoukou 466001,China)

机构地区：[1]郑州轻工业大学数学与信息科学学院,河南郑州450002 [2]周口师范学院数学与统计学院,河南周口466001

出　　处：《数学的实践与认识》2024年第10期231-236,共6页Mathematics in Practice and Theory

基　　金：国家自然科学基金(62003380);博士科研基金(13501050020)。

摘　　要：针对Kou跳扩散模型美式期权定价问题,空间方向采用中心差分格式离散,时间方向采用Rannacher格式离散,并利用简单有效的递推公式近似积分项.采用模超松弛迭代法求解美式期权离散得到的线性互补问题,分析了离散矩阵的性质和算法的收敛条件.数值实验验证了理论分析并表明所构造的方法是有效稳健的.For American option under Kou jump diffusion model,the central difference scheme is used to discretize partial differential operators in spatial direction,Rannacher discrete scheme is used for time derivative,an easy-to-implement recursion formula is employed for the approximation of integral term.For the resulting linear complementarity problems obtained from the discretization of American option are solved by the modulus-based successive overrelaxation(MSOR)iteration method.The property of the system matrix and convergence of the MSOR method are analyzed.Numerical experiments conform theoretical analysis and further show that the proposed method is efficient and robust.

关 键 词：Kou跳扩散模型 美式期权 线性互补问题 模超松弛迭代法 

分 类 号：F830.9[经济管理—金融学] O241.3[理学—计算数学]