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Faculty of Economics

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Ding, Y.

Weak Diffusion Limits of Two Real-Time GARCH-type Models

CWPE20112

Abstract: We derive the diffusion limits of two Real-Time GARCH (RT-GARCH)-type models. We show the diffusion limit of the original RT-GARCH model fails to guarantee with probability one positive volatility unless it is degenerate. Consequently, we propose a novel square-root stochastic heteroskedastic autoregressive volatility (SQ-SHARV) model that builds upon the idea of RT-GARCH while maintaining the usual GARCH diffusion limit. As a result, we call for caution when using RTGARCH since it lacks compatibility with existing asset pricing theories. On the contrary, SQ-SHARV combines the advantages of both RT-GARCH and GARCH models.

Keywords: GARCH, RT-GARCH, SV, diffusion limit

JEL Codes: C22 C32 C58

Author links: Yashuang (Dexter) Ding  

PDF: https://www.econ.cam.ac.uk/research-files/repec/cam/pdf/cwpe20112.pdf

Open Access Link: https://doi.org/10.17863/CAM.62847