本論文探討極值理論於厚尾報酬率下之風險值，結合GARCH模型以捕捉報酬率之條件異質變異。實證上應用極值理論在高信賴水準之下單一資產的風險值估計，獲得準確結果，在納入GARCH模型更充分捕捉資產報酬厚尾與條件異質波動。此外，對於兩資產投資組合，使用Longin (2000)所提出的投資組合風險值模型以極值理論進行兩資產投資組合風險值估算，其與單一資產有同樣的結果。

This thesis studied the extreme value theory on the estimation of the VaR for the financial investment with fat-tailed return distribution. It also explored the GARCH model when it came to model the conditional heteroscedasticity in the financial return data.
Empirical study showed the results that the extreme value theory is useful to accurately estimate VaR for a single asset at high confidence level. It also showed that incorporating a GARCH model for the conditional heteroscedasticity can adequately model the fat tail and heteroscedastical volatility of financial assets.
For the two-asset portfolio, an algorithm proposed by Longin(2000) was used to calculate the VaR for the portfolio. Similar results were obtained as the single –asset portfolio.

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