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Ding, Y.

Diffusion Limits of Real-Time GARCH

WP Number: 2053

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

Author links:

PDF: wp2053.pdf

Open Access Link: 10.17863/CAM.79586

Theme: empirical