Fractional integrated GARCH diffusion limit models

In this paper, we introduce an approximate approach to the fractional integrated GARCH(1,1) model of continuous time perturbed by fractional noise. Based on the L2L2-approximation of this noise by semimartingales, we proved a convergence theorem concerning an approximate solution. A simulation example shows a significant reduction of error in a fractional stock price model as compared to the classical stock price model.