Ding, Y.

Diffusion Limits of Real-Time GARCH

CWPE20112

Abstract: We prove that the diffusion limit of Real-Time GARCH (RT-GARCH) exists if we introduce an auxiliary process to state the system in a Markovian form. The volatility in the diffusion limit follows an Ornstein-Uhlenbeck-type process which fails to be positive with probability one. Moreover, only a degenerate diffusion limit can render an almost surely positive volatility process. As a result, we call for caution when using RT-GARCH since it lacks compatibility with existing asset pricing theories. The result also provides a new insight into how different specifications for GARCH affect its diffusion limit.

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

JEL Codes: C22 C32 C58

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