DefinePK

Abstract

In this article, the classical theory leading to the Black-Scholes equation, widely used in the market model for valuing financial options developed. In this sense, the mathematical development from a stochastic differential equation leads to the equation, Black Scholes; therefore, the model’s solution is presented. Initially, the model is transformed into the heat equation, and then it is combined with the inverse Fourier transformation, supported in the performance of the separation of variables method and the description of the solution according to the nature of the root of the characteristic polynomial. A solution of the call option is achieved. From this, through the parity relation, the value of a put option is also found. Finally, the volatility parameter associated with the model is estimated through the classic and Bayesian approach, where it was shown that when evaluating the premium or price of the option from the volatility estimate from the Bayesian approach, it presents a lower proportion of risk to what happens in the financial market.