Black-Scholes方法的三次三角B-样条配点法

Cubic Trigonometric B-spline Collocation Approach for Black-Scholes Method

摘要:

研究Black-Scholes欧式期权定价模型的三次三角B-样条配点法. 对Black-Scholes方程空间离散采用三次三角B-样条配点法和时间离散采用向前有限差分，并引入参数θ，建立混合差分格式. 利用稳定性分析的Von Neumann (Fourier)方法，证明了该格式当1/2≤θ≤1时是无条件稳定的. 数值实验表明，所构造方法的有效性和准确性，其数值结果优于Crank-Nicolson有限差分法和三次B-样条方法.

Abstract:

A cubic trigonometric B-spline collocation approach is developed for the numerical solution of Black-Scholes equation governing European option pricing. The Black-Scholes equation is fully-discretized using the cubic trigonometric B-spline collocation for spatial discretization and the forward finite difference for the time discretization. A hybrid difference scheme is obtained by means of parameter θ. According to Von Neumann (Fourier) method, it is shown that the presented scheme is unconditionally stable for 1/2≤θ≤1. A numerical experiment is performed to illustrate the validity and accuracy of the proposed method. Moreover, the numerical results are given to show that it is superior to Crank-Nicolson finite difference method and cubic B-spline collocation approach.