Vol. 1 No. 1 (2005)

Artículos

From Bachelier to Merton: 100 Years of the Brownian Motion in Economics and Finance

Published 2005-01-03

  • Francisco Venegas Martínez

Francisco Venegas Martínez
Instituto Tecnológico y de Estudios Superiores de Monterrey-Campus Ciudad de México, Departamento de Finanzas

Abstract

This paper is aimed to review and discuss the contributions from Louis Bachelier, Paul Samuelson, Fischer Black, Myron Scholes, and Robert Merton to continuous-time economics and finance. In their research, the Brownian motion not only provides a suitable modeling of the proper movements of many economic and financial variables, but also it is a very helpful tool to incorporate elements of risk and uncertainty in the dynamic of such variables. Also, the existing relationships between these contributions and the research from other prominent scientists, such as Robert Brown, Albert Einstein, Andrey Markov, Andrei Kolmogorov, Paul Lévy, Norbert Wiener and Kiyosi Itô are discussed. Finally, the paper investigates the evolution of the ideas and formulations of the developed models by Bachelier, Samuelson, Black, Scholes and Merton and simultaneously carries out a comparative analysis among such models.

Keywords

Financial economics, Contingent claims pricing

PDF (Spanish)

References

  1. Bachelier, L. (1900). Théorie de la Spéculation. Tesis de Doctorado en Ciencias Matemáticas, Université Paris Sorbonne, Gauthier-Villars, París.
  2. Bachelier, L. (1964). Theory of Speculation. Traducción de la edición francesa. En: P. H. Cootner (Ed.), The Random Character of Stock Market Prices, Cambridge: MIT Press, pp. 17–78.
  3. Black, F. & Scholes, M. (1973). “The Pricing of Options and Corporate Liabilities”. The Journal of Political Economy, Vol. 81, No. 3, pp. 637–654.
  4. Einstein, A. (1956). Investigations on the Theory of the Brownian Movement. Traducido por A. D. Cowper, Dover Publications, Inc., pp. 12–18.
  5. Merton, R. C. (1973). “Theory of Rational Option Pricing”. Journal of Economic and Management Sciences, Vol. 4, No. 1, pp. 141–183.
  6. Samuelson, P. A. (1965). “Rational Theory of Warrant Prices”. Industrial Management Review, Vol. 6, No. 2, pp. 13–39.
  7. Vasicek, O. (1977). “An Equilibrium Characterization of the Term Structure”. Journal of Financial Economics, Vol. 5, No. 2, pp. 177–188.

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