Evaluation of options using the Black-Scholes methodology

This paper discusses how to obtain the Black-Scholes equation to evaluate options and how to obtain explicit solutions for Call and Put. The Black-Scholes equation, which is the basis for determining explicit solutions for Call and Put, is a rather sophisticated equation. It is a partial differential equation of the second order, parabolic, similar to the heat equation.The terms of the equation express diffusion in a homogeneous environment, convection and reaction. The main objective of the paper is to present the Black-Scholes methodology and apply this methodology on the underlying asset of the nature of the listed stock on the Bucharest Stock Exchange. Also, a secondary objective is to compare the results obtained in this paper with our results in an article where we determined the values for Call and Put by Monte Carlo simulation.