由於風險值模型的理論基礎是奠基於許多簡化的假設之上，無法涵蓋真實環境下所有細節，而且隨著時間及環境的改變，模型結果的正確性也會出現大幅變化；一個成功的模型需要具備有助於預測未來與改善決策過程之效率，即藉由各種情境測試模型之有效性、釐清模型的適用範圍及限制有其必要性。因此本研究以S&P500股價指數為實證對象，研究方法採用GARCH模型波動性估計的T分配法、歷史模擬法，共同建構出包括 GARCH-HS、GARCH-N、GARCH-T等不同的風險值衡量模式，進行金融海嘯前後不同時期風險值模型預測能力之探討，希望能夠將這六種模型適用的範圍界定清楚，使應用者明瞭其限制。

The theory of Value-at-Risk (VaR) is based on several simplified assumptions, which is unable to cover whole detailed situation in reality. The accuracy of the model would be different according the environment. A good model means that it possesses forecasting ability as well as enhancing the efficiency of decision making. In this study, we use the GARCH model with t distribution and historical simulation to investigate the S&P500 index dataset. Several methods are used, including GARCH-HS, GARCH-N, and GARCH-T models, to study the forecasting ability during the financial crisis period. We would like to know how the performance of the six models in analyzing the dataset during crisis period.

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