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

  • Álvaro Javier Cangrejo Universidad Surcolombiana, Neiva
  • Christian Camilo Cortés Universidad Surcolombiana, Neiva
Keywords: Black-Schole Model, fluctuation, European option, Ito lemma, volatility.

Abstract

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.

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Author Biographies

Álvaro Javier Cangrejo, Universidad Surcolombiana, Neiva

MSc(c). Mathematician from the Universidad Surcolombiana (Neiva, Colombia) and candidate to Master in Statistics at the Universidad del Valle (Cali, Colombia)

 

Christian Camilo Cortés, Universidad Surcolombiana, Neiva

Mathematician from the Universidad Surcolombiana (Neiva, Colombia) and Master in Mathematics from the Universidade Federal de Minas Gerais (Belo Horizonte, Brasil) 

References

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.
Published
2017-04-05
Section
Original Research