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Diffusion Limits of Real-Time GARCH


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Working Paper

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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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Publisher

Faculty of Economics, University of Cambridge

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