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

Abstract

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.Convergencia de procesos estocásticos, valuación de derivados, volatilidad estocástica