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Weak Diffusion Limit of Real-Time GARCH Models: The Role of Current Return Information


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Ding, Y. 


We prove that Real-time GARCH (RT-GARCH) models converge to the same type of stochastic differential equations as the standard GARCH models as the length of sampling interval goes to zero. The additional parameter of RT-GARCH can be interpreted as current information risk premium. We show RT-GARCH has the same limiting stationary distribution and shares the same asymptotic properties for volatility filtering and forecast as standard GARCH. Simulation results confirm the current information parameter decreases with the length of sampling interval and hence, GARCH and RT-GARCH models behave increasingly similar for high frequency data. Moreover, empirical results show the current information risk premium has increased significantly after the 2008 financial crisis for S&P 500 index returns.



GARCH, RT-GARCH, SV, diffusion limit, high frequency data

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Faculty of Economics, University of Cambridge

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