投影三角分解法定价带随机波动率的美式期权  

Projected triangular decomposition method for pricing American option under stochastic volatility model

作　　者：郑宁[1] 殷俊锋[1] 徐承龙[1,2] 

机构地区：[1]同济大学数学系,上海200092 [2]上海师范大学,上海高校计算科学E-研究院,"科学计算"上海高校重点实验室,上海200234

出　　处：《应用数学与计算数学学报》2013年第1期114-127,共14页Communication on Applied Mathematics and Computation

基　　金：国家自然科学基金资助项目(11271289;11171256);上海市教育委员会E-研究院建设计划资助项目(E03004)

摘　　要：考虑数值求解Heston随机波动率美式期权定价问题,通过在空间方向采用中心差分格式离散二维偏微分算子,在时间方向利用隐式交替方向格式,将美式期权定价问题转化成求解每个时间层上的若干个线性互补问题.针对一般美式期权定价模型离散得到的线性互补问题,构造出投影三角分解法进行求解,并在理论上给出算法的收敛条件.数值实验表明,所构造的数值方法对于求解美式期权定价问题是有效的,并且优于经典的投影超松弛迭代法和算子分裂方法.For pricing American options using Heston＇s stochastic volatility model center difference schemes and alternative direction implicit schemes are proposed for the space and time discretization of the two-dimensional parabolic partial dif- ferential operator, and the projected triangular decomposition methods are constructed to solve the resulted linear complementarity problems in each time step. The convergence conditions are analyzed when the system matrix is an M-matrix.Numerical experiments confirm the theoretical analysis, and further show that the proposed methods outperform the classical projected iterative methods in computational efficiency.

关 键 词：Heston随机波动率模型 美式期权 隐式交替方向格式 线性互补问题 投影算法 收敛性 

分 类 号：O211.6[理学—概率论与数理统计]