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


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  • Francisco Venegas-Martínez

    (Escuela Superior de Economía, IPN)

  • Francisco J. Sánchez-Torres

    (Escuela Superior de Economía, IPN)


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.

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Bibliographic Info

Article provided by Tecnológico de Monterrey, Campus Ciudad de México in its journal Revista de Administración, Finanzas y Economía (Journal of Management, Finance and Economics).

Volume (Year): 2 (2008)
Issue (Month): 2 ()
Pages: 92-103

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Handle: RePEc:ega:rafega:200807

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Related research

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

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