隨著全球經濟環境的自由化及投資工具的不斷創新，投資人與金融機構所需承擔的風險也比以往更大，國際間因衍生性金融商品的不當操縱而導致鉅額虧損的案例更是時有所聞。近來更由於美國次貸風暴的爆發，造成全球金融危機不斷擴大，外匯市場波動加劇，顯示外匯之風險控制也變得格外重要了。
風險值(Value at Risk, VaR)是當前最廣受運用且能有效衡量風險的工 具。實證研究顯示，大部分的資產報酬皆有厚尾(fat-tailed)及波動叢聚(Volatility)的現象，因此在常態分配假設下的風險值模型可能會低估極端損失發生的可能性。而以極值理論衡量風險值的好處是不需對資產報酬分配做任何假設，只需估計資產的尾部分配，不僅大幅降低模型風險，亦可較準確估計極端事件發生時的最大可能損失。
本研究的主要目的是以2000/01/01到2008/12/31，歐元、英鎊、美元及韓元之每日匯率為研究樣本，利用Bensalah(2002)提出的模擬資產投資組合權重的概念，結合極值理論(Extreme Value Theory, EVT)中的超越門檻值(Peak over Thresholds, POT)模型估計外匯投資組合風險值，進一步找出風險最小下外匯投資組合中每一資產之最適權重，期望透過有效的風險控制及資產配置來降低投資組合的最大可能損失。
實證結果顯示，當資產數為兩種時，相關性較低的兩資產較能有效分散投資組合風險，而資產數為三種時，當隨機抽取之投資組合數超過3,000組時，其風險值已很穩定。

With the liberalization of the global economic environment and the constant innovation of investment tools, investors and financial institutions have come to bear greater risks. From time to time, the misuse of financial derivatives products causes severe international losses. Recently, as a result of the sub-prime mortgage, the global financial crisis continues to expand, market fluctuations of the foreign exchanges are aggravated, revealing the importance of the risk control of the foreign exchanges.
Currently, value at risk (VaR) is a widely used and the most effective tool in measuring risk. A number of empirical studies have illustrated that most asset returns are fat-tailed and demonstrate volatility clustering phenomenon; therefore, the normal distribution assumption underlying the VaR model could lead the VaR model to underestimate the probability of extreme losses. Consequently, the advantage of using extreme value theory (EVT) is that it does not require any assumption; only the tails of the asset returns distribution are estimated, thus reducing the model risk and estimating more precisely the maximum potential loss of extreme events.
The propose of this article is to use Bensalah’s (2002) suggestion to construct a simulated portfolio model combine the peak over thresholds (POT) model of an EVT to measure the VaR for foreign exchanges portfolio. We select the Euro Dollar, British Pound, US dollar and Korean Won during 2000/01/01~2008/12/31 as our empirical samples. Wish through the control for risk efficiency and asset allocation to reduce the maximum potential loss.
The empirical results show that a portfolio with two lowly correlated assets has more diversified benefits. However the VaR will approach stability in a three-asset portfolio as the number of random sampling portfolios exceeds 3,000 groups.

第一章 緒論
第一節 研究背景與動機..................................................................1
第二節 研究目的..............................................................................2
第三節 研究架構..............................................................................3
第二章 文獻回顧..........................................................................................5
第三章 研究方法
第一節 風險值................................................................................15
第二節 極值理論............................................................................19
第三節 極值理論在投資組合風險值上的應用.............................30
第四章 實證結果與分析
第一節 樣本選取與基本統計量分析.............................................33
第二節 估計投資組合風險值........................................................36
第三節 風險最小下之資產配置....................................................39
第五章 結論與建議
第一節 結論....................................................................................49
第二節 後續研究建議....................................................................50
參考文獻........................................................................................................51
V
表目錄
表2.1 風險值國外相關文獻綜合整理.......................................................10
表2.1 風險值國外相關文獻綜合整理(續) ................................................11
表2.1 風險值國外相關文獻綜合整理(續) ................................................12
表2.2 風險值國內相關文獻綜合整理.......................................................13
表2.2 風險值國內相關文獻綜合整理(續) ................................................14
表4.1 各國貨幣兌台幣日報酬率之敘述統計量.......................................36
表4.2 各國貨幣兌台幣日報酬率之相關係數矩陣...................................39
表4.3 投資組合1 之門檻值、GPD 參數之基本統計量及風險值...........40
表4.4 投資組合2 之門檻值、GPD 參數之基本統計量及風險值...........40
表4.5 投資組合1 在99％信心水準下之最適權重..................................41
表4.6 投資組合2 在99％信心水準下之最適權重..................................42
表4.7 投資組合1 在99.9％信心水準下之最適權重...............................43
表4.8 投資組合2 在99.9％信心水準下之最適權重...............................43
表4.9 投資組合1 在99.99％信心水準下之最適權重.............................44
表4.10 投資組合2 在99.99％信心水準下之最適權重.............................45
表4.11 投資組合2 與其它二種貨幣之相關係數矩陣...............................45
表4.12 投資組合3 在99％信心水準下之最適權重..................................46
表4.13 投資組合3 在99.9％信心水準下之最適權重...............................47
表4.14 投資組合3 在99.99％信心水準下之最適權重.............................48
V I
圖目錄
圖1.1 研究流程圖........................................................................................4
圖3.1 風險值定義圖..................................................................................17
圖3.2 BMM 選取之極端樣本....................................................................20
圖3.3 POT 選取之極端樣本......................................................................21
圖3.4 GPD、Exponential 及Beta 分配圖.................................................24
圖3.5 估計投資組合風險值之流程圖.......................................................32
圖4.1 美元兌台幣日報酬率......................................................................34
圖4.2 英鎊兌台幣日報酬率......................................................................34
圖4.3 歐元兌台幣日報酬率......................................................................34
圖4.4 韓元兌台幣日報酬率......................................................................34
圖4.5 美元日報酬率之QQ-Plot................................................................35
圖4.6 英鎊日報酬率之QQ-Plot................................................................35
圖4.7 歐元日報酬率之QQ-Plot................................................................35
圖4.8 韓元日報酬率之QQ-Plot................................................................35
圖4.9 持有英鎊68%，歐元32%之樣本平均餘額函數圖.......................37
圖4.10 模型配適度診斷..............................................................................38

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