状态转换下美式跳扩散期权的修正Crank-Nicolson拟合有限体积法  

A Modified Crank-Nicolson Fitted Finite Volume Method for American Options Under Regime-Switching Jump-Diffusion Processes

作　　者：甘小艇 江忠东 李保荣[3] GAN Xiaoting;JIANG Zhongdong;LI Baorong(School of Mathematical Sciences,Universitay of Electronic Science and Technology of China,Chengdu 611731;School of Mathematics and Statistics,Churiong Normal University,Chuxiong 675000;School of Information Science&Technology,Churiong Normal University,Chuxiong 675000)

机构地区：[1]电子科技大学数学科学学院,成都611731 [2]楚雄师范学院数学与统计学院,楚雄675000 [3]楚雄师范学院信息与计算科学学院,楚雄675000

出　　处：《系统科学与数学》2021年第1期178-196,共19页Journal of Systems Science and Mathematical Sciences

基　　金：国家自然科学基金(61463002);云南省地方本科高校(部分)基础研究联合专项面上项目(2019FH001-079);云南省教育厅科学研究基金项目(2019J0396);楚雄师范学院校级重点科研项目(XJZD1802)资助课题。

摘　　要：主要研究了一类状态转换下美式跳扩散期权定价模型的修正Crank-Nicolson拟合有限体积法并且给出收敛性分析.文章所构造的新方法是对[Gan X T,Yin J F,Li R,Fitted finite volume method for pricing American options under regime-switching.jump-diffusion models based on penalty method.Adv.Appl.Math.Mech.,2020,12(3):748-773]中时间方向上Crank-Nicolson格式的改进.同时,还对求解非线性系统迭代方法的收敛性证明进行了补充.最后,数值实验验证了新方法的有效性.In this paper,we study a modified Crank-Nicolson fitted finite volume method for American options under regime-switching jump-diffusion model and present the convergence analysis.The proposed new method is a modified of the CrankNicolson time-stepping scheme in(Gan,et al.2020).Meanwhile,we supplement the proof of convergence of iterative solution method that has been designed to solve the nonlinear algebraic systems.Finally,numerical experiments are presented to illustrate the efficient of the modified method.

关 键 词：美式期权定价 状态转换跳扩散期权 拟合有限体积法 CRANK-NICOLSON格式 

分 类 号：O241[理学—计算数学]