Diffusion Limits of Real-Time GARCH

Yashuang Ding

Cambridge Working Papers in Economics from Faculty of Economics, University of Cambridge

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 (search for similar items in EconPapers)
JEL-codes: C22 C32 C58 (search for similar items in EconPapers)
Date: 2020-11-25
New Economics Papers: this item is included in nep-ecm, nep-ets and nep-ore
Note: yd274
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Persistent link: https://EconPapers.repec.org/RePEc:cam:camdae:20112

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