風險值的預測－不同模型間的比較

本研究針對國際間的股票市場為實證對象，採用GARCH模型、RiskMetrics模型、歷史模擬法、複合法、QML GARCH模型與極值理論結合QML GARCH這六種模型，來估計因股價損失率變動所預期遭受的最大可能損失，並藉由TUFF、非條件覆蓋率與條件覆蓋率檢定VaR的準確性。　　在往前預測一期時，GARCH模型、RiskMetrics模型、QML GARCH模型與極值理論結合QML GARCH都表現得不錯。以個別資料來看，澳洲全股、英國金融時報100及臺灣加權之資料適合採用QML GARCH與極值理論結合QML GARCH這兩種模型；RiskMetrics、QML GARCH或極值理論結合QML GARCH模型在法國CAC 40、S&P 500和新加坡星股海峽資料中表現良好；道瓊工業的資料則建議使用GARCH或RiskMetrics模型；香港恆生的資料在有母數及半母數的模型中皆表現得不錯，較不建議使用歷史模擬法與複合法；使用RiskMetrics與QML GRACH模型預測那斯達克的VaR能得到不錯的結果。　　到了往前預測兩期時，所有資料在覆蓋率為0.05與0.1的虛無假設下都表現得不好。在虛無假設為0.01時，歷史模擬法與複合法的表現最佳，極值理論結合QML GARCH的表現則是最差的。GARCH型式的模型表現不佳，推測可能是與往前預測的期數增加有關，或是模擬的次數不夠，亦或資料的樣本外個數不夠多。以個別資料來看，澳洲全股與法國CAC 40的資料以歷史模擬法和複合法的表現最好；道瓊工業則是在99%的信賴區間下建議使用歷史模擬法與QML GARCH模型；英國金融時報100以歷史模擬法與GARCH模型表現較好；香港恆生、新加坡星股海峽與史坦普500只建議使用複合法；那斯達克的資料只有歷史模擬法較能準確預測；台灣的資料則是建議使用複合法與GARCH模型。

關鍵字

風險值、GARCH、RiskMetrics、歷史模擬法、複合法、QML GARCH、

並列摘要

This research aims at the stock market of international as substantial evidence object and adopts the GARCH, RiskMetrics, Historical Simulation (HS), Hybrid, QML GARCH and the combination of QML GARCH and EVT (EVT for short). We use this six models to estimate the maximum potential loss due to the volatility and we use the TUFF test, the unconditional coverage test and the conditional coverage test to evaluate the accuracy of VaR. The GARCH, RiskMetrics and EVT model perform well at 1-day ahead. With each stock separately, AORD, FTSE and TW can fitted by the QML GARCH and EVT model; The performance of RiskMetrics, QML GARCH or EVT model are good in the FCHI, S& P 500 and STI data; GARCH and RiskMetrics model are suggested to fit the DJI data; Parametric models and nonparametric models perform well at the HIS but we didn’t suggest to use HS and Hybrid model; Using RiskMetrics and QML GARCH model to forecast the VaR of NASDAQ can get a good result. All the data didn’t perform well under the hypothesis of coverage rate is 0.05 or 0.1 at 2-days ahead. The HS and Hybrid model are the best model but the EVT is the worst model under the hypothesis of coverage rate is 0.01. The performance of GARCH family wasn’t well which conjecture that may be with the forecast period increasing or the number of simulation isn’t enough or the number of out of sample isn’t enough. With each stock separately, the AORD and FCHI data perform well at the HS and Hybrid model; The DJI was suggested using HS and QML GARCH model under 99% confidence level; The FTSE perform well in the HS and GARCH model; The HIS, STI and S&P 500 only suggest using Hybrid model; Only the HS model can estimate accurately at the NASDAQ; The data of TW was suggested to use Hybrid and GARCH model.