陳宏臺灣大學：數學研究所黃以達Huang, Yi-TaYi-TaHuang2007-11-282018-06-282007-11-282018-06-282007http://ntur.lib.ntu.edu.tw//handle/246246/59465風險值為一個普遍應用在財務金融領域上的統計方法，主要用以量化並評估財務市場風險的大小。此篇論文中，我們主要的目的是想尋求由Boudokh,Richardson and Whitelaw於一九九八年所提出一種評估風險值的無母數方法 ─ 複合法的方法特性。在某些正規條件下，本文證明了利用複合法所得到的估計式並非是一致估計式。因此，本文提供一種修正的方法，稱之為校正複合法，其為複合法及歷史模擬法之加權平均。藉由權重之選取，得以提高複合法在估計風險值之精準度。除此之外，我們亦使用實證資料及具波動叢聚性質下之計量模型之模擬資料，來闡述及比較複合法與校正複合法之優劣性。VaR(Value at Risk) is a method of assessing risk that uses standard statistical techniques routinely used in other technical fields. In this thesis, we focus on finding the characteristics of hybrid approach proposed in Boudokh, Richardson and Whitelaw (1998) which is a nonparametric approach for estimating VaR. Under some regular conditions, we prove that the resulting estimator is not consistent. We then propose a modified approach, which is called the modified hybrid approach, to increase its precision. We also demonstrate the pros and cons of the hybrid approach and modified hybrid approach by using some evaluation criteria under various different models and some empirical datas.1 Introduction ......................................1 2 VaR Methodologies .................................4 2.1 Risk Metrics ....................................4 2.2 Historical Simulation ...........................5 2.3 Extreme Value Theory Approach ...................6 3 Hybrid Approach and Its Properties ................9 3.1 The Estimate Based on Hybrid Approach ...........9 3.2 Inconsistency of Hybrid Estimator ..............10 3.2.1 Natural Bound of Hybrid Estimator ............10 3.2.2 Maximal of (r1,r2,...,rK1) and Inconsistency..11 3.3 A Modi.ed Hybrid Estimator .....................11 4 Two Evaluation Criteria ..........................13 5 Performance Analysis under Three Different Models.15 5.1 Stochastic Volatility Models ...................15 5.2 Integrated GARCH(1,1) Models ...................17 5.3 Stochastic Volatility Models with Structural Breaks..18 5.4 Summary ........................................19 6 Empirical Results ................................20 7 Conclusion .......................................25 8 Appendix .........................................26 8.1 Appendix A .....................................26 8.2 Appendix B .....................................27 8.3 Appendix C .....................................30 8.4 Appendix D: Tables .............................32 8.4.1 Simulation Results ...........................32 8.4.2 Empirical Results ............................44 Bibliography700070 bytesapplication/pdfen-US風險值複合法校正複合法歷史模擬法Value at Riskhybrid approachmodified hybrid approachhistorical simulationthesishttp://ntur.lib.ntu.edu.tw/bitstream/246246/59465/1/ntu-96-R92221011-1.pdf