  In this research, we proposed a Mean Convection Finite Difference Method
(MCFDM) for European options pricing. The Black-Scholes model, which describes
the dynamics of a financial asset, was first transformed into a
convection-diffusion equation. We then used the finite difference method to
discretize time and price, and introduced a tuning parameter to enhance the
convection term. Specified the boundary and initial conditions for call and put
options of European options, and performed numerical calculations to obtain a
numerical solution and error estimation. By varying the strength of the strike
price and risk-free interest rate, we explored the accuracy and stability of
our predicted prices. Finally, we compared our proposed method with those
obtained using the Crank-Nicolson Finite Difference Method (CFDM) and Monte
Carlo method. Our numerical results demonstrate the efficiency and accuracy of
our proposed method, which outperformed the CFDM and Monte Carlo methods in
terms of accuracy and speed.
