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
