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研究生:周業熙
研究生(外文):Yeh-Shi Chow
論文名稱:GARCH-type模型在VaR之應用
論文名稱(外文):Application of GARCH-type model at VaR
指導教授:林建甫林建甫引用關係
指導教授(外文):Chien-Fu Jeff Lin
學位類別:碩士
校院名稱:東吳大學
系所名稱:經濟學系
學門:社會及行為科學學門
學類:經濟學類
論文種類:學術論文
論文出版年:2002
畢業學年度:90
語文別:中文
論文頁數:99
中文關鍵詞:涉險值EWMAGARCHGARCH-MEGARCH回溯測試RMSE
外文關鍵詞:VaREWMAGARCHGARCH-MEGARCHback testingRMSE
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隨著我國加入WTO與國際清算銀行(BIS)公佈將於2005年後將風險控管列為強制性的規範,涉險值(VaR)已成為國內外目前最熱門的討論主題之一。但是文獻中發現大多數金融資產報酬率的實際分配具有厚尾(fat-tail)現象,要改善VaR可能低估實際的未來涉險值的情形,本研究嘗試深入探討由GARCH-type模型推估之變異數與共變異數矩陣是否可以改進傳統VaR計算方法的可能性。經本文實證研究後顯示,持有單一個別股票資產時GARCH-type模型對於變異數具有較佳的預測能力,有助於提升VaR的準確性;在投資組合時以GARCH(1,1)-M與AR(1)-EGARCH(1,0)的績效最好,且由於GARCH(1,1)-M模型具有風險貼水的參數,所以可以解釋為台灣股票市場的報酬率與報酬率本身之波動有關,而AR(1)-EGARCH(1,0)模型則可以衡量股票市場中顯著的不對稱效果,因此本文建議以此兩種模型取代傳統之EWMA法與一般用來改善EWMA法之GARCH模型,此為本文貢獻之一。由於金融機構或一般公司之投資部門投資組合在實務應用上包含資產種類眾多,即使在多變量GARCH模型加入某些限制條件後也不太可能估計超過10種個別資產以上的模型參數,所以本文以類似風險矩陣計算共變異數矩陣的設定,求算投資組合各模型所對應的共變異數矩陣,經本文實證結果發現以GARCH(1,1)-M及AR(1)-EGARCH(1,0)模型配合本文對共變異數矩陣的設定除了可以解決多變量GARCH模型在處理種類較多的困難外,也可以有效改善傳統方法對投資組合VaR的預測能力,此為本文貢獻之二。
Along with Taiwan enters WTO and BIS announces that risk management will be constrained regulation after 2005, calculation of VaR has became a hot topic in the world. However, literatures report that the empirical distributions of return in most of financial assets have fat-tail phenomenon. To remedy the under-estimated VaR problem, this study tries to investigate whether the estimation of variance and covariance matrix by GARCH-type model can improve traditional calculation of VaR. The empirical results show that the GARCH-type model have better forecast ability on variance and covariance matrix and improve the accuracy of VaR when holding a single stock asset. The GARCH(1,1)-M and AR(1)-EGARCH(1,0) model perform better in the portfolio analysis. Using the risk premium parameter in GARCH(1,1)-M model, it provides a connection between return rate and volatility in Taiwan stock market. In contrast, the AR(1)-EGARCH(1,0) model can measure the significant asymmetric effect in stock market. In general, this research recommends GARCH(1,1)-M and AR(1)-EGARCH(1,0) models to replace EWMA method or traditional GARCH model in calculating VaR. This is the first contribution in this study. Moreover, banking institutes and investment section of general companies usually process numerous categories of assets in practical portfolio. Multivariate GARCH model would not be possible to estimate the parameters that exceeding 10 kinds of asset after adding some restricted conditions. Thus this paper sets the approach of covariance matrix like RiskMetricTM to compute portfolio’s covariance matrix in each model. The empirical results show that the GARCH(1,1)-M and AR(1)-EGARCH(1,0) model with the setting of covariance matrix not only solves the difficulty when multivariate GARCH model deals with massive portfolio, but also improves the forecast of portfolio’s VaR in the traditional way. This reveals the second contribution in this study.
第一章 緒論 1
1.1 研究背景與動機 1
1.2 研究問題與目的 5
1.3 研究流程與架構 6
第二章 文獻回顧 8
2.1 涉險值之定義與計算 8
2.2 涉險值模型之文獻探討 11
2.3 驗證涉險值的方法 26
第三章 研究方法 29
3.1 指數權數移動平均法(EWMA) 35
3.2 GARCH-type模型 40
3.2.1 AR(1)-GARCH(1,1)模型 42
3.2.2 GARCH(1,1)-M模型 44
3.2.3 AR(1)-EGARCH(1,0)模型 45
3.3 金融資產間共變異數矩陣或相關係數矩陣之預測方法 48
3.4 比較各模型所預測之VaR的方法 49
3.4.1 回溯測試(back testing) 49
3.4.2 方均根誤法(root mean squared error) 50
3.4.3 概似比檢定(LR test) 51
第四章 實證研究 53
4.1 資料檢驗 54
4.2 使用限制 59
4.3 估計結果 60
4.4 資產組合VaR之計算 63
4.5 實證分析 64
4.5.1 單一個別資產 66
4.5.2 投資組合 73
第五章 結論與建議 81
5.1 結論 81
5.2 建議 83
參考文獻 85
附錄 89
附錄A EWMA法估計模型之衰退參數 的選擇程序 89
附錄B 違反時間平方根法則(square root of time rule)的例子91
附錄C 本研究撰寫之相關RATS程式 92
[中文部分]
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[英文部分]
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