Options valuation analysis of the shares of Ecopetrol and Pacific Exploration between June 2013 and July 2016

Álvaro Javier Cangrejo, Christian Camilo Cortés


In this paper, we analyze the environment and the dynamics of the Black-Scholes model starting from a stochastic differential equation that explains the evolution of the future prices of an asset. With these defined guidelines, the data obtained by the daily closing prices between June 2013 and June 2016 of the shares of Ecopetrol and Pacific Exploration are normalized, by means of a Box-Cox transformation, to determine the volatility of each of them and apply this model to calculate the value of the asset with fixed time, and thus determine which of the two oil companies have a lower risk at the time of investing.


Black-Schole Model; fluctuation; European option; Ito lemma; volatility.

Full Text:



Castillo B. (2012). El modelo de Black-Scholes de valoración de opciones financieras [tesis]. Universidad de Barcelona: España.

Elliott, R.J. & Kopp, P.E. (1999). Mathematics of financial markets. New York, NY: Springer.

Farlow, S. (1993). Partial differential equations. New York, NY: Dover.

Garcia, J.A. (2008). Matemáticas financieras con ecuaciones de diferencia finita [5a ed.]. Bogotá, Colombia: Pearson.

Kozikowski, Z. (2007). Matemáticas financieras: el valor del dinero en el tiempo. México DF: McGraw-Hill.

Serrano, J. & Villareal, J. (1993). Fundamentos de finanzas [2a ed.]. Bogotá, Colombia: McGraw-Hill.

DOI: http://dx.doi.org/10.18046/syt.v15i40.2390


  • There are currently no refbacks.