In this paper, we consider a class of a nonlinear option pricing models considering transaction costs. The focus is on the numerical investigation of the Delta equation, where the unknown is the first spatial derivative of the option value. A numerical algorithm for solving a generalized Black–Scholes partial differential equation, which arises in European option pricing considering transaction costs is studied. The Crank–Nicolson method used to discretize in the temporal direction and the FEM used to discretize in the spatial direction are discussed in terms of accuracy, convergence and efficiency. The efficiency and accuracy of the proposed method are tested numerically, and the results confirm the theoretical behavior of the solutions, which are also found to be in good agreement with the exact solution of the linear case.