三次B-样条配点法定价欧式看跌期权  

Cubic B-spline Collocation Method for Pricing European Put Option

作　　者：吴蓓蓓[1,2] WU Beibei 1,2(1. School of Mathematics Science, Tongji University, Shanghai 200092 ; 2. School of Mathematics and Physics, Shanghai University of Electric Power, Shanghai 20009)

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：《四川师范大学学报（自然科学版）》2018年第2期246-251,共6页Journal of Sichuan Normal University（Natural Science）

基　　金：国家自然科学基金(11271289和11502141)

摘　　要：基于重新定义的基函数,给出了Black-Scholes模型下欧式看跌期权定价的三次B-样条配点法.利用这种改进的三次B-样条配点法和有限差分法离散Black-Scholes偏微分方程,并对差分格式的稳定性进行分析,得到稳定性条件.数值实验表明,所构造方法的准确性,有效地提高了计算效率,且其Crank-Nicolson格式的数值结果要优于隐式欧拉格式.A cubic B-spline collocation method is proposed for pricing Black-Scholes European put option model based on redefined basis functions. The Black-Scholes partial differential equation is discreted with this improved cubic B-spline collocation method and the finite difference method. The stability of difference scheme is analyzed and a stability condition is obtained. The results of a numerical experiment illustrate the accuracy of the constructed method,which improves the calculation efficiency. It is shown that the Crank-Nicolson scheme is better than the implicit Euler scheme.

关 键 词：欧式看跌期权 BLACK-SCHOLES方程 三次B-样条 有限差分 

分 类 号：O241.8[理学—计算数学]