Deducción de la ecuación de back – scholes en un contexto de precios estocásticos

Abstract

Those who negotiate options in the stock market know the risks to which they are exposed, hence the importance of mathematics in the valuation of financial derivatives. The purpose of this document is to study the Black - Scholes model and present the deduction for European call options. The theoretical basis of the model goes to the theory of stochastic calculus, which operates in stochastic processes and stochastic differential equations for modeling systems that behave randomly. With the intention of carrying out the simulation in Python of valuation situations of European call-type options, the data of the closing prices of the shares of the Corficolombiana financial corporation in the period from November 2018 to October 2019 were collected from the Bolosa de Valores de Colombia. A quantitative methodology was used for the analysis of these data in order to obtain the necessary information in the formulation of the parameters of the equation for the simulation. The results obtained evidenced the efficiency of the Black - Scholes model in determining the fair price of an option at a future date under the parameters established in the equation in a context of stochastic prices. The values reached in the simulation of the model turned out to be a good approximation to the real costs of an option in the stock market.