許多研究指出金融市場具有條件波動不對稱的特性，必須利用非對稱GARCH模型來捕捉此一現象，在眾多的非對稱GARCH模型中，以GJR GARCH模型表現較好。本研究比較結合GJR GARCH模型之跳躍擴散隨機過程與極值理論在台灣加權指數與美國S&P 500指數之風險值估算結果，實證指出在台灣加權指數之風險值估算，以跳躍擴散隨機過程結合GJR GARCH模型表現最佳；而在S&P 500指數之風險值估算上，以極值理論之廣義極值分配結合GJR GARCH模型有較好之結果。

Many studies point out that the financial markets have characteristics of the asymmetry of the conditional volatility. The asymmetric GARCH models have been used to catch this phenomenon. The GJR GARCH model is the most used model for the asymmetry of the conditional volatility. This thesis studies the extreme value theory with the jump diffusion stochastic process that incorporates GJR GARCH model on the estimation of the VaR for the TWII and S&P 500 index and concludes that the jump diffusion stochastic process incorporating a GJR GARCH model has the best result on the estimation of the VaR for TWII. But for the S&P 500 index, the Generalized extreme value distribution incorporating a GJR GARCH model is more appropriate for the estimation of the VaR.

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