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Diffusion Limits of Real-Time GARCH

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  • 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.

Suggested Citation

  • Ding, Y., 2020. "Diffusion Limits of Real-Time GARCH," Cambridge Working Papers in Economics 20112, Faculty of Economics, University of Cambridge.
    • Handle: RePEc:cam:camdae:20112
    Note: yd274
    as

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    References listed on IDEAS

    as
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    More about this item

    Keywords

    GARCH; RT-GARCH; SV; diffusion limit;
    All these keywords.

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics

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