In financial markets, accurate option pricing is essential for investors and risk managers. Two widely used mathematical models for pricing European options are the Binomial Option Pricing Model and the Black-Scholes Model. This paper provides a comparative study between the two models by analyzing their assumptions, computational approaches, strengths, and limitations. While the binomial model offers a discrete-time framework and is particularly suitable for American-style options, the Black Scholes model provides a continuous-time analytical solution under specific assumptions. A numerical example is used to illustrate how the two models produce similar results under certain conditions. Numerical results demonstrate that as the number of steps in the Binomial model increases, the results converge significantly toward the Black-Scholes model values, confirming the convergence between discrete and continuous models in financial mathematics.................... Keywords:................. stochastic model, option pricing, black-scholes, binomial model.