臺灣博碩士論文加值系統

本文使用歷史模擬法、GARCH、EGARCH、GJR-GARCH與CARR模型針對紐約商業交易所(New York Mercantile Exchange,NYMEX)天然氣商品(Natural Gas,NG)為研究對象，在誤差項分別假設為常態分配與t分配下計算其風險值，本文嘗試比較不同窗口長度和顯著水準下之模型特性；在模型評估方面，本文利用回朔測試，計算失敗次數、失敗比率，並以Christoffersen (1998)發展之Likelihood Ratio test 分別檢定未受條件限制下與受條件限制下之檢定統計量，衡量各模型績效。經過實証分析後發現，誤差項設定以常態分配較能準確評估天然氣期貨資產特性，失敗比率上五種模型都有不錯的表現，隨著顯著水準的降低，模型將趨於穩定，在LR test中以CARR與EGARCH模型表現較佳。

This paper use historical simulation approach, GARCH model, EGARCH model, GJR-GARCH model and CARR model, under different error term distribution hypothesis to estimate the Value at Risk of NYMEX Natural Gas price.
　　We use different number of days and significant level to test our model and observe their performance. To value our model, we use back test, calculate failure frequency, failure ratio, and use Christoffersen’s Likelihood Ratio Test to test unconditional and conditional test statistic. According to our analysis, error term should be suppose to normal distribution, that can fit the NYMEX Natural Gas property. The model have good performance in failure ratio, as the significant level goes down, the model will be more stable, CARR and EGARCH model have better performance in LR Test.

目錄
第壹章、緒論……………………………………………………………1
　1.1　研究動機……………………………………………………………………1
　 1.2 研究目的……………………………………………………………………1
1.3 研究架構……………………………………………………………………2
第貳章、文獻回顧………………………………………………………3
2.1 風險值定義…………………………………………………………………3
2.2 風險值估計方法……………………………………………………………3
2.3 模型檢定……………………………………………………………………6
第参章、研究方法………………………………………………………7
3.1 風險值計算…………………………………………………………………7
3.2 風險值模型…………………………………………………………………8
　3.2.1 歷史模擬法……………………………………………………………8
3.2.2 GARCH Model ………………………………………………………9
3.2.3 GJR-GARCH Model ………………………………………………11
3.2.4 EGARCH Model ……………………………………………………12
3.2.5 CARR Model ………………………………………………………13
3.3 風險值模型檢定 …………………………………………………………14
3.3.1 回朔測試 ……………………………………………………………14
3.3.2 失敗比率 ……………………………………………………………15
3.3.3 概似比率法 …………………………………………………………15
3.3.4 RMSE ………………………………………………………………17
第肆章、實證分析 ……………………………………………………19
4.1 資料來源與處理…………………………………………………………19
4.2 基本統計量與相關檢定……………………20
4.3 風險值估計……………………………………………22
第伍章、結論……………………………………………………34

參考文獻 ………………………………………………………………35
附錄一 天然氣價格直方圖……………………………………………37
附錄二 N=500，t-distribution，P&L和風險值走勢圖…………38
附錄三 N=250，t-distribution，P&L和風險值走勢圖…………40
附錄四 N=500，Normal distribution，風險值穿透圖…………42
附錄五 N=500，波動度圖形預測圖………………………………43
附錄六 N=500，t-distribution參數估計………………………45

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