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Sobre la convergencia del modelo GARCH(1,1)-M al movimiento geométrico browniano con reversión a la media


  • Francisco Venegas Martínez

    () (IPN)

  • Francisco J. Sánchez Torres



This paper shows, under certain conditions, the convergence of the GARCH (1.1)-M model to the geometric Brownian motion with mean reversion (diffusion GARCH process). The importance from this result is that the problem of inference on the parameters of the valuation models of options with stochastic volatility can be reduced by estimating the model GARCH (1.1)-M. It is also carried out a discussion on the assumptions that ensure the existence and uniqueness of the limit process. Finally, it is provided a quick demonstration of the convergence, which is less formal, but more intuitive and easy to remember

Suggested Citation

  • Francisco Venegas Martínez & Francisco J. Sánchez Torres, 2008. "Sobre la convergencia del modelo GARCH(1,1)-M al movimiento geométrico browniano con reversión a la media," Revista de Administración, Finanzas y Economía (Journal of Management, Finance and Economics), Tecnológico de Monterrey, Campus Ciudad de México, vol. 2(2), pages 92-103.
  • Handle: RePEc:ega:rafega:200807

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    Convergencia de procesos estocásticos; valuación de derivados; volatilidad estocástica;

    JEL classification:

    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes


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