Black-Scholes模型的三次三角B-样条配点法  

Cubic trigonometric B-spline collocation method for Black-Scholes model

作　　者：吴蓓蓓[1,2] 殷俊锋[1] 金猛[1] WU Bei-Bei;YIN Jun-Feng;JIN Meng(School of Mathematics Science, Tongji University, Shanghai 200092, China;School of Mathematics and Physics, Shanghai University of Electric Power, Shanghai 200090, China)

机构地区：[1]同济大学数学科学学院,上海200092 [2]上海电力学院数理学院,上海200090

出　　处：《四川大学学报（自然科学版）》2017年第6期1153-1158,共6页Journal of Sichuan University(Natural Science Edition)

基　　金：国家自然科学基金(11271289)

摘　　要：本文研究了Black-Scholes欧式期权定价模型的三次三角B-样条配点法.对BlackScholes方程,该方法的空间离散采用三次三角B-样条配点法,时间离散采用向前有限差分,并引入参数θ来建立混合差分格式.利用稳定性分析的Von Neumann(Fourier)方法,本文证明了该格式在1/2≤θ≤1时是无条件稳定的.数值实验显示,该方法的数值结果优于Crank-Nicolson有限差分法和三次B-样条方法.A cubic trigonometric B-spline collocation method is developed for numerical solution of the Black-Scholes equation governing European option pricing. In this method, the Black-Scholes equation is fully-discretized by using the cubic trigonometric B-spline collocation for spatial discretization and the forward finite difference for the time discretization. As a result,a hybrid difference scheme is obtained by introducing the parameter 0. According to the Von Neumann （Fourier） method, the presented method is proven to be unconditionally stable for 1/2≤θ≤1. A numerical experiment is performed to illustrate the validity and accuracy of the method. It is shown that this method is superior to the Crank-Nicolson finite difference method and cubic B-spline collocation.

关 键 词：期权定价 BLACK-SCHOLES方程 三次三角B-样条 有限差分 

分 类 号：O241.8[理学—计算数学]