On a Black–Scholes American Call Option Model

This study focuses on the Black–Scholes American call option model as a moving boundary problem. Using a front-fixing approach, the model is derived as a fixed domain nonlinear parabolic problem, and the uniqueness of both the call option price and critical stock price is established. An iterative approach is established to numerically solve the problem, and the convergence of the iterative method is proved. For computational implementation, a finite difference scheme in conjunction with a second-order Runge–Kutta method is conducted. Finally, the numerical results for two test problems are reported in order to confirm our theoretical achievements.