基于有限差分离散的模方法定价美式债券期权  

Modulus Methods for Pricing American Bond Option Based on Finite Difference Discretization

作　　者：甘小艇 徐登国 豆铨煜[2] GAN Xiaoting;XU Dengguo;DOU Quanyu(School of Mathematics and Statistics,Chuxiong Normal University,Chuxiong 675000,Yunnan Province,China;School of Mathematical Sciences,Tongji University,Shanghai 200092,China)

机构地区：[1]楚雄师范学院数学与统计学院,云南楚雄675000 [2]同济大学数学科学学院,上海200092

出　　处：《吉林大学学报（理学版）》2018年第4期837-844,共8页Journal of Jilin University:Science Edition

基　　金：国家自然科学基金(批准号:61463002);云南省教育厅科学研究项目(批准号:2015Y443);楚雄师范学院学术骨干项目(批准号:XJGG1601)

摘　　要：针对美式债券期权定价模型的数值解法,构造全隐式的有限差分格式,并给出格式的稳定性证明.采用模系矩阵分裂迭代法求解离散得到的线性互补问题,并与投影超松弛迭代法进行比较.数值实验验证了新方法的有效性和稳健性.In view of the numerical solution of American bond option pricing model,we constructed a fully implicit finite difference scheme and proved the stability of the scheme.Then,the modulus-based matrix splitting iteration methods were applied to solve the linear complementarity problems（LCP）,and further compared it with the projected successive overrelaxation（PSOR）iteration method.Numerical experiments verified the effectiveness and robustness of the new methods.

关 键 词：美式债券期权模型 有限差分格式 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]