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研究生:蕭雲心
研究生(外文):YUN-HSIN HSIAO
論文名稱:小波轉換應用於風險值估計
論文名稱(外文):Analysis of Value-at-Risk estimation by Wavelet Transform
指導教授:張桂芳張桂芳引用關係
指導教授(外文):Kuei-Fang Chang
學位類別:碩士
校院名稱:逢甲大學
系所名稱:應用數學所
學門:數學及統計學門
學類:數學學類
論文種類:學術論文
論文出版年:2009
畢業學年度:97
語文別:中文
論文頁數:62
中文關鍵詞:回溯測試離散小波轉換多層解析風險值信賴水準持有期間
外文關鍵詞:Value-at-RiskMultiresolution AnalysisConfidence LevelDiscrete Wavelet TransformBack Testing
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風險值(Value-at-Risk)是現今衡量風險的標準,以預估投資市場資料報酬率。小波轉換對估計報酬率風險型態模型無需作假設,且可針對非線性的報酬率進行多層解析分析。本論文以非鐵金屬類、石油、匯率、基金之資料,利用小波轉換得到數值化的風險模型,藉由小波分析時域與頻率域的高頻資訊,針對不同的持有期間,利用小波轉換做各階層的多層解析分解,得到模型參數進行風險值估計,與真實報酬率比較得到穿透次數,以觀察其估計準確程度。若利用回溯測試法來預測穿透次數未落入可信區間,則改變各階層的相對能量加權值介於0.5至2之間,不同類別資料,有不同的加權值的穩定值,改善穿透次數。對於各階層相對能量加權值的選取,設定一程式碼,只要輸入資料與筆數、加權值區間、信賴水準對應值,則會有適當加權值。另外,以非鐵金屬類為資料,本論文的估計模式於多日逐日預估較WDVaR模型於一日逐日預估的預測績效表現為佳。
Value-at-Risk (VaR) had been a criterion for the investment of market return rates. The wavelet transform does not need assumptions for estimating return rates risk model, and make multiresolution analysis in counter of non-linear return rates. This paper utilizes the data of nonferrous metal, original oil, the exchange rate, and the fund material, using the discrete wavelet transformation to obtain the numerical risk model, using the high frequency data obtain by the wavelet analysis of time and frequency domain countering with different processing period, obtain the model parameter to estimate the return rates by discrete wavelet transformation, then compare it with the real return rates to get the penetrating times to observe the accuracy rate of the estimation. If the forecasting number of exceptions does not fall into the confidence interval in backing test method, then we change the relative energy weight in each level to be between 0.5 to 2, different data categories have different relative energy weight stability to improve penetrating times. As to the relative energy value''s selection at each level, set an algorithm and input the data and numbers, relative energy weight interval, and corresponding value of confidence level, then we get the suitable weight. Moreover, if we take the nonferrous metal for data, the estimated model of multiple-steps ahead forecasts is better than the WDVaR model of one-step ahead forecasts.
目錄......................i
圖目錄....................ii
表目錄....................iii
第一章 緒論..................................................................................................................1
第二章 小波轉換..........................................................................................................3
2.1 多層解析空間...........................................................................................3
2.2 離散小波轉換.......................................................................................... 5
2.2.1 訊號的分解與重建............................................................................5
2.3 Daubechies小波係數建構........................................................................7
第三章 風險值........................................................................................................10
3.1 風險值的意義.........................................................................................10
3.2 風險值估計方法.....................................................................................12
3.3 波動性估計.............................................................................................13
3.4 時間的可加性( Time Aggregation ) ......................................................15
3.5 風險值模型的適合度檢定.....................................................................16
第四章 小波分析預估風險值................................................................................20
4.1 離散小波轉換矩陣表示法.....................................................................20
4.2 變異數的分析.........................................................................................21
4.3 預估小波變異數.....................................................................................23
4.4 小波能量分配估計風險值.....................................................................25
第五章 實驗方法與結果........................................................................................27
5.1 實驗設計與方法.....................................................................................27
5.2 實驗結果與比較.....................................................................................30
5.2.1多日逐日預估.....................................................................................30
5.3 與WDVaR之模型比較..........................................................................48
第六章 未來研究方向..............................................................................................60
參考文獻......................................................................................................................61
[1] A. Boggess and F. J. Narcowich , A First Course in Wavelets with Fourier Analysis , Prentice Hall.,2001.
[2] R.Gencay, F. Selcuk, and B. Whitcher, An introduction to Wavelets and Other Filtering Methods in Finance and Economics, Academic Press, San Diego, 2003.
[3] C.W.J. Granger,” Non-Linear Models: Where Do We Go Next -Time Varying Parameter Models?”, Studies in Nonlinear Dynamics & Econometrics, 12(2008), Issue 3,1-9.
[4] K. He, C. Xie, and K. K. Lai, “Estimating Real Estate Value-at-Risk Using Wavelet Denoising and Time Series Model”, Lecture Notes In Computer Science, 5102(2008),494-503.
[5] B. James, “Ramsey Wavelets in Economics and Finance: Past and Future”,(2002),C.V. Starr Center for Applied Economics, NYU Working Paper No. S-MF-02-02, http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1300227
[6] P. Jorion, Value at Risk: The New Benchmark for Controlling Market Risk, McGraw-Hill Companies, Inc.,1997.
[7] P. Jorion, Value at Risk: The New Benchmark for Managing Financial Risk, McGraw-Hill Companies, Inc.,2007.
[8] K. K. Lai , K. He, C. Xie and S. Chen, “Market Risk for Nonferrous Metals: A Wavelet Based VaR Approach”, IEEE, 1( 2006), 1178-1184,.
[9] B. Roger and Z. Jennifer ,“Beyond the short run: The longer time scale volatility of investment value”, (2006),http://eprints.otago.ac.nz/606/.
[10] H. Yuri, Wavelet-based Value At Risk Estimation, Erasmus University Rotterdam, Master thesis Informatics and Economics, 2003.
[11]李元,時間序列中變點的小波分析及非線性小波估計,中國統計出版,2002,北京。
[12]李進生等,風險管理:風險值(VaR)理論與應用, 清蔚科技股份有限公司,2001,台北市。
[13]單維彰,凌波初步,全華科技圖書公司,1999,台北市。
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