臺灣博碩士論文加值系統

合理之涉險值量化模型應以機率理論中之最大順序統計量(maximum order statistic)的觀點出發，並依據極端值理論(extreme value theory)建構出涉險值之可能分配形態。此種理念不但可去除不合理之常態分配假設，而且可以精確地捕捉金融資產報酬之肥尾現象，並進一步了解損失與發生機率間的對應關係，成為壓力測試(stress testing)執行之參考。Danielsson與de Vries(1997)所提出之半參數型極端涉險值估計模型，利用半參數估計法結合歷史資訊，以構建出投資組合報酬率分配左端之累積機率密度函數，並可用以構建適當之壓力情境機率計量模型。惟該模型參數之拔靴估計程序必須仰賴電腦模擬以進行樣本之隨機抽樣(random sampling)，鑒於藉助一般套裝軟體發展的亂數產生器(random number generator)產生的亂數群所具有之群聚(clustering)現象將降低涉險值估計之精確性並增加參數估計之均方差(mean squared error, MSE)。緣此，本研究擬利用準亂數(quasi-random)產生器之修正技術，改進Danielsson與de Vries(1997)之半參數型極端涉險值估計模型，期能增進估計效率及降低估計偏誤，並有效捕捉投資組合之下方風險。

Accurate prediction of the frequency of extreme events is of primary importance in many financial applications such as Value-at-Risk (VaR) analysis. We improve the estimation procedure of the semi-parametric method that is announced by Danielsson and de Vries (1997) for VaR evaluation. For estimations and predictions of low probability worst outcomes, semi-parametric method has to apply the Hall’s (1990) subsample bootstrap methods. However in the procedure of subsample bootstrap, the estimates obtained from applying the pseudo-random numbers are less accurate and efficient in the VaR prediction. We propose a new quasi-random sampling technique, which is very useful for applications of semi-parametric method. Quasi-random sampling technique use sequences that are deterministic instead of random. These sequences will improve the convergence of extreme VaR estimation. In addition, we both use the backtesting and stress testing method to evaluate the performance of extreme VaR estimation. Finally, we also prove that why Basle Committee on Banking Supervisory set the lowest scaling factor as 3.

第一章 緒論
第一節 研究背景與動機
第二節 研究問題與目的
第三節 研究流程
第四節 論文架構
第二章 文獻探討
第一節 變異數--共變異數法
第二節 蒙地卡羅模擬法
第三節 歷史模擬法
第四節 國內相關文獻
第三章 研究方法
第一節 半參數型極端涉險值模型
第二節 準亂數抽樣技術
第三節 回溯測試
第四節 本研究所使用方法論之流程
第四章 實證結果與分析
第一節 蒙地卡羅模擬實驗
第二節 準亂數抽樣技術之改進情形
第三節 回溯測試結果
第四節 亞洲金融危機與壓力測試
第五章 結論與建議
第一節 結論
第二節 後續建議
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