利用優質與劣質波動度進行波動度預測

Abstract

本篇論文以拆解變異數的方式延伸文獻上的波動度模型，並使用延伸之模型去預測S&P500指數的波動度。我們參考Corsi (2009)提出的HAR模型和Blair et al. (2001)提出的ARCH模型進行延伸，並將延伸後的多個模型分別歸類為HAR模型類別和ARCH模型類別。樣本內估計結果顯示，在HAR模型類別中未來波動度和劣質波動度的相關性高於優質波動度，在ARCH模型類別中各種延伸與拆解都能顯著提升模型表現。樣本外預測結果顯示，在HAR模型類別中將隱含變異數加入HAR模型預測效果最好，在ARCH模型類別中將已實現變異數或隱含變異數加入Glosten et al. (1993)所提出的GJR模型中預測表現最佳。

We forecast the volatility of the S&P500 Index by extending models through the way of decomposing variance measures into good and bad components. HAR model of Corsi (2009) and ARCH models shown in Blair et al. (2001) are extended in HAR model class and ARCH model class respectively. The in-sample estimation shows that future volatility is more strongly related to the volatility of past negative returns than to that of positive returns in HAR model class, and each kind of decomposition and extension in ARCH models leads to significant model improvement. For out-of-sample forecasting, we find that adding implied variance in HAR models provides the most accurate forecasts in HAR model class and that the inclusion of realized variance or implied variance as an explanatory variable in the GJR model outperforms other models in ARCH model class.