Heterogeneous Volatility Information Content for the Realized GARCH Modeling and Forecasting Volatility
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Wen Xu
,
Pakorn Aschakulporn
Abstract
As the demand for accuracy in volatility modeling and forecasting increases, the literature tends to incorporate different volatility measures with heterogeneous information content to construct the hybrid volatility model. This study focuses on one of the popular hybrid volatility models: the Realized Generalized Autoregressive Heteroskedasticity (Realized GARCH) and embeds various volatility measures, including the CBOE VIX, VIX1D, Realized Volatility, and Daily Range to examine their heterogeneous impact on the conditional volatility estimation and forecasting. To evaluate the impact of the volatility measures, we first construct a volatility response function. This involves calculating the difference in one-step-ahead conditional volatility forecasts that incorporate information from both return and volatility measures against the forecasts based on return innovations only. Subsequently, the variance share is calculated to evaluate its role in explaining future variations in the Realized GARCH. Our results show that among these four volatility measures, VIX is the most informative volatility. Although VIX1D is overemphasized by the literature, its significance in volatility forecasting remains substantial, confirming that risk-neutral volatility measures are generally more informative than physical measures. Finally, we also find that incorporating multiple risk-neutral volatility measures does not improve forecasting performance compared to using a single measure due to overlapping information.
Acknowledgment
We are especially grateful to an anonymous reviewer whose helpful comments substantially improved the paper. Wen Xu is particularly grateful to Yu Zhou for his research support. He appreciates having interesting discussions with Jungah Yoon, Jianhui Li, Junyu Zhang, Weihan Li, Ruizi Hu, and Tianjiao Li during our regular Derivatives and Quantitative Finance Group meetings. He also appreciates being awarded the University of Otago Doctoral Scholarship. Jin E. Zhang has been supported by an establishment grant from the University of Otago.
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Author contributions: Wen Xu: Writing and Editing, Data Allocations and Processing, Conceptualization, Software; Pakorn Aschakulporn: Review and Editing, Supervision, Conceptualization; Jin E. Zhang: Review and Editing, Supervision, Conceptualization, Funding Acquisition.
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Conflict of interest statement: The author declares no conflicts of interest regarding this article.
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Research funding: This work was funded by an establishment grant from the University of Otago.
Granger causality test.
| Null hypothesis | P value |
|---|---|
| VIX1D does not Granger Cause VIX | 0.1521 |
| VXF does not Granger Cause VIX | 0.0138 |
| VIX does not Granger Cause VIX1D | 0.0000 |
| VXF does not Granger Cause VIX1D | 0.0250 |
| VIX does not Granger Cause VXF | 0.0097 |
| VIX1D does not Granger Cause VXF | 0.0977 |
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This table presents the Granger Causality test based on the VAR model. VXF denotes the nearest term VIX futures price, which is constructed based on the exchange-traded contracts provided by the CBOE.
Variance share.
| VIX | VIX1D | RV | DR |
|---|---|---|---|
| Panel A: Pairwise impact | |||
| 97.08 % | 2.92 % | – | – |
| 91.65 % | – | 8.35 % | – |
| 99.63 % | – | – | 0.37 % |
| – | 34.50 % | 65.50 % | – |
| – | 99.19 % | – | 0.81 % |
| – | – | 97.59 % | 2.41 % |
| Panel B: System level impact | |||
| 64.59 % | 16.68 % | 18.73 % | – |
| 99.31 % | 0.69 % | – | <0.01 % |
| 77.14 % | – | 19.93 % | 2.93 % |
| – | 27.04 % | 68.04 % | 4.92 % |
| 61.05 % | 12.87 % | 25.84 % | 0.24 % |
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This table presents variance shares in the Realized GARCH framework, showing how various volatility measures contribute to the future variance of log h t . Percentages reflect the relative impact of RVt+1, DRt+1, VIX1D t , and VIX t .
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