Abstract:

In this paper, we investigates the numerical solution of the Black-Scholes equation for European option pricing using an exponential time differencing (ETD) approach. The governing partial differential equation is discretized in space by a finite difference scheme, which transforms the problem into a system of ordinary differential equations in time. The ETD method is then applied to efficiently integrate the resulting system. Numerical experiments for European call and put options are presented to illustrate the accuracy and stability of the proposed scheme. The results demonstrate that the ETD-finite difference approach provides an efficient numerical framework for solving the Black--Scholes model.