本篇文章主要研究在不同長短的估計期間下，風險值績效表現是否會因而有所影響。研究標的採用美國道瓊工業指數於次級房貸風暴發生時期進行風險值評估。在模型配適部分利用平均-變異數模型與AR(1)-GARCH(1,1)配適，由於傳統統計推論假設資料是服從常態分配，但經過大量的實證研究證明金融資料的特性其實非常態，故將波動模型之誤差項設定為一般化偏態t分配，並與常態分配分別比較估計結果。而估計方法則以有無採用拔靴法計算信賴區間做區分，融入移動視窗概念估計變異數動態參數過程，以利提升估計風險值的準確度。
   實證結果顯示當估計期間為250天，在回溯測試檢定或者是模型正確性檢定下，兩者的風險值績效表現都略低於估計期間較長的情況，也就代表進行風險值評估時，須要針對估計期間加以考量，且以採取長天期的估計期間較能夠有效的正確估計風險值，但估計期間設定過長則可能會發生資料存在結構性轉變的情況，故本研究提供風險管理者於實務上應針對期間設定加以分析，以提升風險值的績效表現。

This thesis examines different estimation periods that would affect the performance of VaR. Because of the reports of the Basel committee, estimating VaR should be performed on a long and short term basis. As such, the estimation periods will be 250 days, 500 days and 750 days in this thesis. The empirical data applies to the Dow Jones Industrial Average historical return rate that is provided to compare the performance of each model. We will also use the GARCH model, capturing heteroskedasticity effects to increase suitability. Also taking into account the characteristics of financial data, we use generalized skewed t distribution to evaluate the VaR, comparing it with normal distribution. The estimation method applies a rolling bootstrapping method to obtain an appropriate confidence interval.
   The empirical results demonstrate that, in both the back and LR testing, the performance of 250 days is worse compared to longer term periods. Consequently, this shows that using longer estimation period is superior to shorter term estimation. Concerning the empirical results, it is important to consider the difference of estimation periods to assess VaR. Empirical results provide greater accuracy in VaR forecasting. However, empirical results would require structure changes in long estimation periods. Hence, this thesis offers the conception of choosing estimation periods in order to increase performance. This technique is aimed to be helpful to investors or risk managers to make appropriate strategies.

目錄		IV
表目錄		V
圖目錄		VII
第一章	緒論	1
第一節	研究背景與動機	1
第二節	研究目的	3
第三節	研究架構	5
第四節	研究流程	6
第二章	文獻回顧	7
第一節	風險值定義	8
第二節	風險值估計方法	10
第三節	國外相關文獻	14
第四節	國內相關文獻	19
第三章	研究方法	22
第一節	波動模型之參數估計	22
第二節	風險值實證模型	25
第三節	拔靴法估計步驟	30
第四節	模型配適檢定方法	31
第四章	實證結果與分析	36
第一節	資料來源	36
第二節	基本統計與資料處理	37
第三節	波動模型參數估計結果	41
第四節	風險值之估計結果	48
第五章	結論與建議	63
參考文獻	65
中文文獻	65
英文文獻	66


表目錄
表4.2.1  美國道瓊工業指數之敘述統計	39
表4.2.2  美國道瓊工業指數報酬率之單根檢定	40
表4.2.3  美國道瓊工業指數之LM檢定	41
表4.3.1  參數估計結果-估計期間250天	44
表4.3.2  參數估計結果-估計期間500天	45
表4.3.3  參數估計結果-估計期間750天	46
表4.4.1  風險值估計結果	48
表4.4.2  回溯測試與LR檢定估計結果-估計期間250天	55
表4.4.3  回溯測試與LR檢定估計結果-估計期間500天	56
表4.4.4  回溯測試與LR檢定估計結果-估計期間750天	57
表4.4.5  回溯測試實證結果	58
表4.4.6  LR檢定實證結果	58
表4.4.7  RMSE比較表	59

 
圖目錄
圖1.1   研究架構流程圖	6
圖2.1   風險值機率密度函數圖	10
圖3.1.1  SGT分配與常態分配機率密度函數圖	29
圖4.2.1  美國道瓊工業指數與報酬率走勢圖	38
圖4.3.1  SGT分配與Normal分配機率密度函數實證結果圖	47
圖4.4.1  風險值回溯測試結果圖-估計期間250天	60
圖4.4.2  風險值回溯測試結果圖-估計期間500天	61
圖4.4.3  風險值回溯測試結果圖-估計期間750天	62

 

參考文獻
中文文獻

1.田瀅嫆，(2006)，厚尾分配下風險值與ETL探討─穩定分配與一般化誤差分配之應用，銘傳大學財務金融學系碩士論文。
2.李命志，李彥賢，張智超，(2005)，原油價格風險值的估計—拔靴法的應用，金融風險管理季刊，第1卷，第2期，57-74頁。
3.周業熙，(2002)，GARCH-type模型在VaR之應用，東吳大學經濟學系碩士論文。
4.邱登揚，(2009)，全球金融海嘯下之風險值為基礎的商品市場風險管理令人信服嗎?，淡江大學財務金融學系碩士論文。
5.洪瑞成，(2002)，風險值之探討-對稱與不對稱波動GARCH模型之應用，淡江大學財務金融學系碩士論文。
6.高櫻芬，謝家和，(2002)，涉險值之衡量--多變量GARCH模型之應用，經濟論文叢刊， 第30輯，第3期。
7.郭貞伶，(2002)，金融控股公司經營績效評估之研究，國立中山大學財務管理研究所碩士論文。
8.陳佳琪，(2008)，原油價格波動性預測，淡江大學財務金融學系碩士論文。
9.黃美慈，(2010)，資料頻率與風險值估計，逢甲大學風險管理與保險學系碩士論文。
10.劉洪鈞，(2008)，波動性預測與風險管理，淡江大學財務金融學系博士班學位論文。
 
英文文獻

1.Alexander, C. O., and Leigh, C. T. (1997). On the covariance matrices used in Value at Risk models, Journal of Derivatives, 4, pp.50-62.
2.Bali, T. G., and Neftci, S. (2003). Disturbing extremal behavior of spot rate dynamics, Journal of Empirical Finance, 10, pp.455-477.
3.Bali, T. G., and Theodossiou, P. (2007). A conditional-SGT-VaR approach with alternative GARCH models, Annals of Operations Research, 151, pp.241-267.
4.Bali, T. G., Mo, H., and Tang, Y. (2008). The role of autoregressive conditional skewness and kurtosis in the estimation of conditional VaR, Journal of Banking and Finance, 32, pp.269-282.
5.Beder, T. S. (1995). VaR: Seductive but dangerous, Finance Analysts Journal, 51, pp.12-24.
6.Billio, M., and Pelizzon, L. (2000). Value-at-Risk: A multivariate switching regime approach, Journal of Empirical Finance, 7, pp.531-554.
7.Black, F., Jensen, M., and Scholes, M. (1972). The capital asset pricing model: Some empirical tests. Studies in the theory of capital markets, 81, pp.79-121.
8.Chan, W. H., and Maheu, J. M. (2002). Conditional jump dynamics in stock market return, Journal of Business and Economic Statistics, 20, pp.377-389.
9.Christoffersen, P. F. (1998). Evaluating interval forecasts, International Economic Review, 39, pp.841-862.
10.Christoffersen, P., and Goncalves, S. (2005). Estimation risk in financial risk management, Journal of Risk, 7, pp.1-28.
11.Drew, L. (1997). Value-at-Risk: Valuable tool for riskier times, Journal of Lending and Credit Risk Management, 79, pp. 23-29.
12.Efron, B. (1979). Bootstrap methods: Another look at the jackknife, Annals of Statistics, 7, pp. 1-26.
13.Efron, B., and Tibshirani, R. (1993). An introduction to the bootstrap, New York: Chapman and Hall.
14.Engle, R. F. (1982). Autoregressive conditional heteroscedasticity with estimates of variance of United Kingdom inflation, Econometrics, 50, pp.987-1007.
15.Fisher, R. A., and Tippett, L. H. C. (1928). Limiting forms of the frequency distribution of the largest or smallest member of a sample, Proceedings of the Cambridge Philosophical Society, 24, pp.180-190.
16.Giot, P., and Laurent, S. (2003). Value at Risk for long and short positions, Journal of Applied Econometrics, 18, pp.641-663.
17.Hansen, B. E. (1994). Autoregressive conditional density estimation, International Economic Review, 35, pp.705-730.
18.Hansen, P. R., and Lunde, A. (2005). A forecast comparison of volatility models: does anything beat a GARCH (1, 1)? Journal of Applied Econometrics, 20, pp.873-889.
19.Harris, R. D. F., Kucukozmen, C. C., and Yilmaz, F. (2004). Skewness in the conditional distribution of daily equity returns, Applied Financial Economics, 14, pp.195-202.
20.Hendricks, D. (1996). Evaluation of Value-at-Risk models using historical data, Economic Policy Review, 2, pp.39-69.
21.Hill, B. M. (1975). A simple general approach to inference about the tail of a distribution, Annals of Statistics, 3, pp.1163-1174.
22.Jondeau, E., and Rockinger, M. (2003). Conditional volatility, skewness, and kurtosis: Existence and persistence, Journal of Economic Dynamics and Control, 27, pp.1699-1737.
23.Jorion, P. (1996). Risk: Measuring the risk in Value at Risk, Financial Analysts Journal, 52, pp.47-56.
24.Jorion, P. (2000). Value at Risk: The new benchmark for managing financial risk, 2nd Edition, New York: McGraw-Hill.
25.Jorion, P., and Khoury, S. J. (1996). Financial risk management: Domestic and international dimensions, Blackwell.
26.JP Morgan Guaranty Trust Company (1996). RiskMetrics─Technical Doucment, 4th ed, New York
27.Kupiec, P. (1995). Techniques for verifying the accuracy of risk measurement models, Journal of Derivatives, 3, pp.73-84.
28.Lintner, J. (1965). The valuation of risk assets and the selection of risky investments in stock portfolios and capital budgets, Review of Economics and Statistics, 47, pp.13-37.
29.Longin, F. M. (2000). From Value at Risk to stress testing: The extreme value approach, Journal of Banking and Finance, 24, pp.1097-1130.
30.Markowitz, H. (1952). Portfolio selection, Journal of Finance, 7, pp.77-91.
31.McNeil, A. J., and Frey, R. (2000). Estimation of tail-related risk measures for heteroscedastic financial time series: An extreme value approach, Journal of Empirical Finance, 7, pp.271-300.
32.Ross, S. A. (1976). The arbitrage theory of capital asset pricing, Journal of Economic Theory, 13, pp.341-360.
33.Seymour, A. J., and Polakow, D. A. (2003). A coupling of extreme-value theory and volatility updating with Value-at-Risk Estimation in emerging markets: A south african test, Multinational Finance Journal, 7, pp.3-23.
34.Sharpe, W. F. (1964). Capital asset prices: A theory of market equilibrium under conditions of risk, Journal of Finance, 19, pp.425-442.
35.Siegl, T., and West, A. (2001). Statistical bootstrapping methods in VaR calculation, Applied Mathematical Finance, 8, pp.167-181.
36.Theodossiou, P. (1998). Financial data and the skewed generalized t distribution, Management Science, 44, pp.1650-1661.
37.Thombs, L. A., and Schucany, W. R. (1990). Bootstrap prediction intervals for autoregression, Journal of the American Statistical Association, 85, pp.486-492.