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

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.