Diffusion Limits of Real-Time GARCH
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Authors
Ding, Y.
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.
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Keywords
GARCH, RT-GARCH, SV, diffusion limit
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Faculty of Economics, University of Cambridge