In this paper, we establish Reconstructed Variational Iteration Method (RVIM), in combination with the Laplace transform for the Black-Scholes option pricing model for the first time. We derive exact solutions for two types of BSM. The first equation is a transformed version of the classical BSM, while the second is a generalized BSM where volatility is modeled as a function of the underlying stock price. The solutions obtained through RVIM have been thoroughly validated against existing results in the literature, demonstrating strong agreement. Additionally, we provide 2-Dimensional and 3-Dimensional graphical representations of the solutions, offering further insights into their behavior. This study confirms the effectiveness of RVIM in solving both classical and generalized Black-Scholes equations.