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| 研究生： |
黃之澔 |
|---|---|
| 論文名稱： |
預測S&P500指數實現波動度與VIX－ 探討VIX、VIX選擇權與VVIX之資訊內涵 The S&P 500 Index Realized Volatility and VIX Forecasting - The Information Content of VIX, VIX Options and VVIX |
| 指導教授： |
陳威光
Chen, Wei Kuang 林靖庭 Lin, Ching Ting |
| 學位類別： |
碩士
Master |
| 系所名稱： |
商學院 - 金融學系 Department of Money and Banking |
| 論文出版年： | 2015 |
| 畢業學年度： | 103 |
| 語文別： | 英文 |
| 論文頁數： | 42 |
| 中文關鍵詞： | VIX 選擇權 、VVIX 、資訊內涵 、S&P500指數實現波動度 、動態轉換模型 、風險中立動差 |
| 外文關鍵詞： | VIX Options, VVIX, Information Content, S&P 500 Realized Volatility, Regime Switching Model, Risk Neutral Moments |
| 相關次數： | 點閱：123 下載：27 |
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波動度對於金融市場影響甚多，同時為金融資產定價的重要參數以及市場穩
定度的衡量指標，尤其在金融危機發生時，波動度指數的驟升反映資產價格震盪。
本篇論文嘗試捕捉S&P500 指數實現波動度與VIX變動率未來之動態，並將VIX、
VIX 選擇權與VVIX 納入預測模型中，探討其資訊內涵。透過研究S&P500 指數
實現波動度，能夠預測S&P500 指數未來之波動度與報酬，除了能夠觀察市場變
動，亦能使未來選擇權定價更為準確；而藉由模型預測VIX，能夠藉由VIX 選
擇權或VIX 期貨，提供避險或投資之依據。文章採用2006 年至2011 年之S&P500
指數、VIX、VIX 選擇權與VVIX 資料。
在 S&P500 指數之實現波動度預測當中，本篇論文的模型改良自先前文獻，
結合實現波動度、隱含波動度與S&P500 指數選擇權之風險中立偏態，所構成之
異質自我回歸模型(HAR-RV-IV-SK model)。論文額外加入VIX 變動率以及VIX指數選擇權之風險中立偏態作為模型因子，預測未來S&P500 指數實現波動度。
研究結果表示，加入VIX 變動率作為S&P500 指數實現波動度預測模型變數後，
可增加S&P500 指數實現波動度預測模型之準確性。
在 VIX 變動率預測模型之中，論文採用動態轉換模型，作為高低波動度之
下，區分預測模型的方法。以VIX 過去的變動率、VIX 選擇權之風險中立動差
以及VIX 之波動度指數(VVIX)作為變數，預測未來VIX 變動率。結果顯示動態
轉換模型能夠提升VIX 預測模型的解釋能力，並且在動態轉換模型下，VVIX 與
VIX 選擇權之風險中立動差，對於VIX 預測具有相當之資訊隱涵於其中。
This paper tries to capture the future dynamic of S&P 500 index realized
volatility and VIX. We add the VIX change rate and the risk neutral skewness of VIX
options into the Heterogeneous Autoregressive model of Realized Volatility, Implied
Volatility and Skewness (HAR-RV-IV-SK) model to forecast the S&P 500 realized
volatility. Also, this paper uses the regime switching model and joins the VIX, risk
neutral moments of VIX options and VVIX variables to raise the explanatory ability
in the VIX forecasting. The result shows that the VIX change rate has additional
information on the S&P 500 realized volatility. By using the regime switching model,
the VVIX and the risk neutral moments of VIX options variables have information
contents in VIX forecasting. These models can be used for hedging or investment
purposes.
1. Introduction 1
2. Literature Review 2
2.1 VIX, VIX Options and VVIX 2
2.2 Risk Neutral Skewness 3
2.3 HAR-RV-IV-SK Model 4
2.4 Volatility Forecasting 4
2.5 Regime Switching Model 5
3. Data 6
3.1 CBOE Data 6
3.2 Realized Volatility Data 7
3.3 VIX Options Data 7
3.4 Risk Neutral Moments of VIX Options 7
3.5 VVIX Data 10
4. S&P 500 Realized Volatility Forecasting 12
4.1 Single Variable Regression Testing 12
4.2 Methodology 13
4.3 Results 18
4.4 Residual Analysis 20
5. VIX Forecasting 23
5.1 Single Variable Regression Testing 24
5.2 Regime Switching Model 25
5.3 VIX Forecasting Models 26
5.4 VIX Forecasting Results 31
5.5 Model Analysis 33
6. Conclusion 36
Appendix I – The formula of VIX 38
Appendix II – The formula of risk neutral moments of VIX options 39
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