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.

翻译：本文提出了一种用于欧式期权定价的平均对流有限差分方法（MCFDM）。首先将描述金融资产动态的Black-Scholes模型转换为对流扩散方程，然后采用有限差分法对时间和价格进行离散化，并引入调谐参数来增强对流项。针对欧式看涨期权和看跌期权，我们规定了边界条件和初始条件，通过数值计算获得数值解及误差估计。通过改变行权价和无风险利率的强度，我们探究了预测价格的准确性和稳定性。最后，我们将所提方法与Crank-Nicolson有限差分方法（CFDM）和蒙特卡罗方法进行了比较。数值结果表明，所提方法在精度和速度上均优于CFDM和蒙特卡罗方法，具有高效性和准确性。