臺灣博碩士論文加值系統

近年釵h研究應用極值理論於風險值估計，但傳統極值理論假設序列之間為完全獨立，不符合現實社會中的情況。本研究希望利用極端指數修正極值理論的序列相關問題，以求得更準確的風險值。我們以八個新興市場的國際股價指數為樣本，利用回饋測試估算樣本外的預測風險值後與實際報酬率相較計算超限率，比較極值理論與不同模型績效。

研究結果顯示以極端指數修正極值理論後，極值理論風險值模型的績效表現比起未修正時要來的好；並且在高分量下的風險值績效表現，比動態極值理論的GARCH-GEV模型來的好。

Extreme value approach was broadly used to calculate value-at-risk recently. Traditional extreme value theory derived from independent process, but it is unrealistic, especially for financial asset returns. The purpose of this paper is to overcome this difficulty with extremal index that makes extreme value theory could derived from dependent process. Our sample includes daily stock indices of eight emerging markets over period 1993-2006. Using backtesting of historical return series, we compare performances of different methods.

The result shows that extreme value approach performs better with correction of extremal index. And compare to GARCH-GEV model of conditional extreme value theory, extreme value approach with extremal index performs better at high quantiles.

目錄
1 序論 1
1.1 研究動機………………………………………………………………….....1
1.2 研究目的.........................................................................................................2
1.3 研究架構.........................................................................................................2
2 文獻回顧 3
2.1 風險值.……………………………………………………………................3
2.2 研究不同風險值模型績效文獻.....................................................................4
3 理論探討 5
3.1 極值理論.……………………………………………………………............5
3.1.1 極值分配.……………………………………………………….......6
3.1.2 極值參數估計....................................................................................7
3.1.2.1 有母數法.............................................................................8
3.1.2.2 無母數法...........................................................................10
3.2 極端指數. .……………………………………………………………........11
3.2.1 雙門檻波動指數.……………………………………………….....13
3.2.2 雙門檻波動指數估計.………………………………………….....14
4 研究方法 15
4.1 極值理論風險值.………………………………………………………......15
4.2 估計極值參數.……………………………………………………………..16
4.3 估計極端指數.……………………………………………………………..17
4.4 回饋測試.……………………………………………………………..........17
4.5 其他估計風險值模型.…………………………………………………......18
4.5.1 變異數－共變異數法.………………………………………….....18
4.5.2 歷史模擬法.…………………………………………………….....18
4.5.3 GARCH-GEV法.……………………………………………….....19
5 實證結果與分析 20
5.1 資料來源與敘述統計.…………………………………………………......20
5.2 極值參數估計.……………………………………………………………..21
5.3 極端指數估計值.…………………………………………………………..22
5.4 回饋測試.……………………………………………………………..........23
5.4.1 極端指數修正後的GEV模型績效.…………………………….....23
5.4.2 修正後的GEV 模型與GARCH－GEV 模型比較.………….....25
6 結論 27
參考文獻 29



圖表目錄
表一：八個新興市場股價指數日報酬率敘述統計....................................................32
表二：極值分配參數估計值........................................................................................33
表三：三種門檻下的極端指數....................................................................................34
表四：未做修正的GEV與三種模型績效比較...........................................................35
表五：95%門檻值下的GEV與三種模型績效比較...................................................35
表六：90%門檻值下的GEV與三種模型績效比較...................................................36
表七：85%門檻值下的GEV與三種模型績效比較...................................................36
表八：95%門檻值下的GEV與GARCH-GEV模型績效比較...................................37
表九：90%門檻值下的GEV與GARCH-GEV模型績效比較...................................37
表十：85%門檻值下的GEV與GARCH-GEV模型績效比較...................................38
圖一：區段樣本極大值QQ-plot..................................................................................39
圖二：區段樣本極小值QQ-plot..................................................................................40

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