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.

本系統係藉由分析歷史交易資料來預測S&P500期貨市場之漲幅。 我們改進了Tsaih et al. (1998)提出的混和式AI系統。 該系統結合了Rule Base 系統以及類神經網路作為其預測之機制。我們針對該系統在以下幾點進行改善：(1) 將原本的日期資料改為使用分鐘資料作為輸入。(2) 本研究採用了“移動視窗”的技術，在移動視窗的概念下，每一個視窗我們希望能夠在60分鐘內訓練完成。(3)在擴增了額外的變數 – VIX價格做為系統的輸入。(4) 由於運算量上升，因此本研究利用TensorFlow 以及GPU運算來改進系統之運作效能。 我們發現VIX變數確實可以改善系統之預測精準度，但訓練的時間雖然平均低於60分鐘，但仍有部分視窗的時間會小幅超過60分鐘。 / The system is made to predict the Futures’ trend through analyzing the transaction data in the past, and gives advices to the investors who are hesitating to make decisions. We improved the system proposed by Tsaih et al. (1998), which was called hybrid AI system. It was combined with rule-based system and artificial neural network system, which can give suggestions depends on the past data. We improved the hybrid system with the following aspects: (1) The index data are changed from daily-based in into the minute-based in this study. (2) The “moving-window” mechanism is adopted in this study. For each window, we hope we can finish training in 60 minutes. (3) There is one extra variable VIX, which is calculated by the VIX in this study. (4) Due to the more computation demand, TensorFlow and GPU computing is applied in our system. We discover that the VIX can obviously has positively influence of the predicting performance of our proposed system. The average training time is lower than 60 minutes, however, some of the windows still cost more than 60 minutes to train.