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系統識別號 U0002-1405200816040800
中文論文名稱 波動性預測與風險管理
英文論文名稱 Volatility Forecasting and Risk Management
校院名稱 淡江大學
系所名稱(中) 財務金融學系博士班
系所名稱(英) Department of Banking and Finance
學年度 96
學期 2
出版年 97
研究生中文姓名 劉洪鈞
研究生英文姓名 Hung-Chun Liu
電子信箱 891490038@s91.tku.edu.tw
學號 891490038
學位類別 博士
語文別 英文
口試日期 2008-05-11
論文頁數 99頁
口試委員 指導教授-李命志
共同指導教授-邱建良
委員-梁發進
委員-許振明
委員-黃彥聖
委員-楊朝成
委員-謝文良
委員-聶建中
中文關鍵字 波動性  風險值  厚尾  GARCH模型  新興市場  能源商品 
英文關鍵字 Volatility  Value-at-Risk  Fat tails  GARCH model  Emerging markets  Energy commodities 
學科別分類 學科別社會科學商學
中文摘要 本論文著重於波動性預測、風險值的衡量以及SGT分配於風險管理之應用,共包含三個部份。第一部份為「GARCH-SGED模型之中國股市波動性預測」、第二部份為「能源商品的風險-厚尾GARCH模型之應用」與第三部份為「SGT分配在風險值估計所扮演的角色」。將此三部份的內容簡述如下。
第一部份使用GARCH-N與GARCH-SGED模型,探討資產報酬率分配的設定對樣本外波動性預測績效的影響。實證資料採取中國兩大股票市場(上海綜合股價指數與深圳綜合股價指數),其用意在於進行大陸新興市場之分析,較一般已開發市場更有趣且更具吸引力。實證結果指出,不論是以MSE或MAE作為比較準則,在不同的預測期間,GARCH-SGED模型對大陸股票市場之波動性預測能力皆優於GARCH-N模型。同時,DM檢定統計量進一步證實GARCH-SGED模型顯著優於GARCH-N模型。此結果隱含具偏態及厚尾特性的分配在波動性預測的重要性,尤其是新興國家的金融市場。
第二部分導出Politis(2004)之厚尾分配(HT-distribution)的臨界值公式,藉由此公式將有助於模型樣本外風險值的計算。實證應用則選取GARCH-N、GARCH-t與GARCH-HT等三個不同分配下的GARCH模型,估計一天的絕對風險值,並比較其在風險管理上的績效表現。本文使用三個模型計算五個能源商品現貨(西德州中級原油、布蘭特原油、熱燃油、丙烷與汽油)的多頭部位風險值,並以準確性及效率性兩個層面進行風險值績效分析。實證結果發現,在資產報酬率具有高峰、厚尾特性下,GARCH-HT模型之風險值估計,於所有信心水準下,均最具準確性。此外,MRSB指出,GARCH-HT在較高的信心水準下,所估計出的風險值亦普遍最具效率性。此結果顯示HT分配,特別在能源商品的風險值估計時,是相當合適的。
第三部份則透過風險值的觀點來評估國際原油市場的風險。本部分以適合捕捉波動性叢聚現象的GARCH模型為基礎,並結合兼具厚尾、高峰及偏態特性之SGT分配建構GARCH-SGT模型來估計西德州中級原油現貨報酬之一日風險值。藉由一系列之風險值績效評估準則,實證結果指出在不同的信心水準下,GARCH-SGT模型所估計之風險值,顯著優於傳統研究經常使用之GARCH-T或GARCH-GED模型。因此,SGT分配之假設確實有助於西德州中級原油之風險值預測,意味著風險值模型,同時考量厚尾、高峰及偏態確有其必要性。此一實證結果提供了GARCH-SGT在風險衡量上,為一穩健之風險值估計方法的有利證據。
英文摘要 The purpose of this dissertation is to contribute to the literature on volatility forecasting and its application to risk management (Value-at-Risk) which comprises three parts. The first part of the dissertation is entitled “Predicting the Volatility of Stock Indices in China using GARCH Models with Skewed-GED Distribution”, the second part is named “Modelling Risk for Energy Commodities via Fat-Tailed GARCH Models”, and the last one is “Daily Volatility Forecasts with Application to Risk Management: The Role of SGT Distribution in VaR Estimation”. A brief introduction of these three parts can be summarized as follows:
The first part investigates how specification of return distribution influences the out-of-sample volatility forecasting performance using GARCH-N and GARCH-SGED models. Illustrations of these techniques are presented for two main stock markets in China, the daily spot prices of Shanghai and Shenzhen composite stock indices, which are considered more interesting and attractive than that of general developed capital markets. Empirical results indicate that the GARCH-SGED model is superior to the GARCH-N model in forecasting China stock markets’ volatility, for alternative forecast horizons when model selection is based on MSE or MAE. Meanwhile, the DM-tests further confirm that volatility forecasts by the GARCH-SGED model are more accurate than those generated using the GARCH-N model in all cases, indicating the significance of both skewness and tail-thickness in the conditional distribution of returns, especially for the emerging financial markets.
In the second part, an analytical quantile-operator of the standard HT distribution (Politis, 2004) is derived which facilitates convenient in out-of-sample VaR estimation with HT distribution. In empirical application, we employ GARCH-N, GARCH-t and GARCH-HT models to estimate the one-day-ahead absolute VaR and compare their performance in risk management of competing models. Daily spot prices of WTI crude oil, Brent crude oil, heating oil #2, propane and Conventional Gasoline Regular are used as empirical data to compare the accuracy and efficiency of these VaR models. Empirical results suggest that for asset returns that exhibit leptokurtic and fat-tailed features, the VaR estimates generated by the GARCH-HT models have good accuracy at both low and high confidence levels. Moreover, MRSB measures indicate that the GARCH-HT model is more efficient than alternatives for most cases at high confidence levels. These findings suggest that the heavy-tailed distribution is more suitable for energy commodities, particularly VaR calculation.
The last part of my dissertation is to contribute to the literature by assessing market risk in the international crude oil market from the perspective of VaR analysis. A GARCH-SGT approach is thus proposed capable of coping with fat-tails, leptokurtosis and skewness using SGT returns innovations and catering for volatility clustering with the GARCH(1,1) model in modeling one-day-ahead VaR. This technique is illustrated using daily returns of West Texas Intermediate crude oil spot prices from December 2003 to December 2007. Empirical results indicate that the VaR forecast obtained by the GARCH-SGT model is superior to that of the GARCH-T and GARCH-GED models through a series of rigorous model selection criteria. Overall, the sophisticated SGT distributional assumption significantly benefits VaR forecasting for WTI crude oil returns at low and high confidence levels, indicating a need for VaR models that consider fat-tails, leptokurtosis and skewness behaviors. This makes the GARCH-SGT model be a robust forecasting approach which is practical to implement and regulate for VaR measurement.
論文目次 TABLE OF CONTENTS
Page
ACKNOWLEDGEMENT i
ABSTRACT IN CHINESE ii
ABSTRACT IN ENGLISH iv
LIST OF TABLES ix
LIST OF FIGURES x

PART I 1
Predicting the Volatility of Stock Indices in China Using GARCH Models with Skewed-GED Distribution

ABSTRACT 2
CHAPTER
1. Introduction 3
1.1 Motivations and Objectives 3
1.2 Flow Chart 5
2. Literature Review 6
3. Econometric Methodology 11
3.1 GARCH(1,1) Model with Normal and Skewed-GED Distributions 11
3.2 Volatility Forecasts 13
3.3 Evaluation of Volatility Forecasting Performance 14
3.3.1 Loss Functions 14
3.3.2 Model Significance Test (DM-Test) 15
4. Data Description and Empirical Results 17
4.1 Data Description 17
4.2 Estimation Results 20
4.3 Volatility Forecasting Performance 22
5. Concluding Remarks 25
BIBLIOGRAPHY 27
PART II 30
Modelling Risk for Energy Commodities via Fat-Tailed GARCH Models

ABSTRACT 31
CHAPTER
1. Introduction 32
1.1 Motivations and Objectives 32
1.2 Flow Chart 34
2. Literature Review 35
3. Econometric Methodology 40
3.1 The GARCH Models with Alternate Conditional Distributions 40
3.1.1 GARCH(1,1) Model with Normal Distribution (GARCH-N) 40
3.1.2 GARCH(1,1) Model with Student t Distribution (GARCH-t) 41
3.1.3 GARCH(1,1) Model with Heavy-Tailed Distribution (GARCH-HT) 42
3.2 Evaluation Methods of Model-Based VaR 44
3.2.1 Binary Loss Function (BLF) 44
3.2.2 Quadratic Loss Function (QLF) 45
3.2.3 LR Test for Unconditional Coverage (LRuc) 45
3.3 Mean Relative Scaled Bias (MRSB) 46
4. Data Description and Preliminary Analysis 48
4.1 Data Description 48
4.2 Preliminary Analysis 48
5. Empirical Results and Analyses 53
5.1 Estimates for the GARCH-N, GARCH-t and GARCH-HT models 53
5.2 Accuracy and Efficiency Measurements 56
5.2.1 VaR Performance for Low Confidence Levels 56
5.2.2 VaR Performance for High Confidence Levels 59
6. Conclusions and Implications 62
APPENDIX 64
BIBLIOGRAPHY 65

PART III 68
Daily Volatility Forecasts with Application to Risk Management: The Role of SGT Distribution in VaR Estimation

ABSTRACT 69
CHAPTER
1. Introduction 70
1.1 Motivations and Objectives 70
1.2 Flow Chart 73
2. Literature Review 74
3. Econometric Methodology 78
3.1 Conditional Volatility Model 78
3.2 Alternative Distributions 79
3.3 Calculating Value-at-Risk 80
3.4 Evaluating VaR Performance of Competing Models 81
3.4.1 Unconditional Coverage Test (LRuc) 81
3.4.2 Conditional Coverage Test (LRcc) 81
3.4.3 Risk Management Loss Functions 82
3.4.3.1 Regulatory Loss Function (RLF) 83
3.4.3.2 Firm Loss Function (FLF) 83
3.4.3.3 Superiority Tests in Terms of Utility-Based Loss Functions 84
4. Data and Empirical Results 85
4.1 Data Description 85
4.2 Estimation Results and Diagnostic Tests 88
4.3 Analysis of VaR Performance 90
4.3.1 Unconditional and Conditional Coverage Tests Results 90
4.3.2 Model Selection Based on Utility-Based Loss Functions 92
5. Conclusions 95
BIBLIOGRAPHY 97



LIST OF TABLES
Page
PART I

Table I.1. Descriptive Statistics of Stock Indices in China 19
Table I.2. Unit Root Tests of Stock Indices in China 20
Table I.3. Estimation Results of Alternate GARCH Models 21
Table I.4. Out-of-Sample Mean Squared Error Statistic 22
Table I.5. Out-of-Sample Mean Absolute Error Statistic 23
Table I.6. DM-Test Results 24

PART II

Table II.1. Descriptive Statistics of Daily Returns 49
Table II.2. Estimation Results of Alternate GARCH(1,1) Models 55
Table II.3. Forecasting Performance Summary for Different VaR Models at Low
Confidence Levels 58
Table II.4. Forecasting Performance Summary for Different VaR Models at High
Confidence Levels 60

PART III

Table III.1. Summary Statistics of Crude Oil Returns 86
Table III.2. Estimation Results for Alternatively Competing VaR Models 89
Table III.3. Forecasting Performance Summary of Value-at-Risk Statistics 91
Table III.4. Superiority Tests in Terms of Utility-Based Loss Functions at the
95% Confidence Level 94




LIST OF FIGURES
Page
PART I

Figure I.1. Descriptive Graphs of Stock Indices in China 18
Figure I.2. Skewed-GED Density Against the Normal Distribution 22

PART II

Figure II.1. Energy Commodities in Levels for Whole Sample 50
Figure II.2. Density of the Daily Returns v.s. Normal Distribution for Whole Sample 51
Figure II.3. The Rolling Window Scheme of the One-Day-Ahead Out-of-Sample
VaR Forecasts 53

PART III

Figure III.1. Descriptive Graphs of WTI Crude Oil 87
Figure III.2. Daily Returns and Alternative Model-Based VaR Forecasts 92
參考文獻 BIBLIOGRAPHY
Akgiray, V., 1989. Conditional heteroskedasticity in time series of stock return: Evidence and forecasts. Journal of Business 62, 55-80.
Awartani, B. M. A., Corradi, V., 2005. Predicting the volatility of the S&P-500 stock index via GARCH models: The role of asymmetries. International Journal of Forecasting 21, 167-183.
Bali, T. G., 2007. Modeling the dynamics of interest rate volatility with skew fat-tailed distributions. Annals of Operations Research 1, 151-178.
Bekaert, G., Wu, G., 2000. Asymmetric volatility and risk in equity markets. Review of Financial Studies 13, 1-42.
Black, F., 1976. Studies of stock prices volatility changes. Proceedings of the 976 Meeting of the American Statistical Association, Business and Economic Statistics Section, 177-181.
Bollerslev, T., 1987. A conditional heteroskedastic time series model for speculative prices and rates of return. Review of Economics and Statistics 69, 542-547.
Bollerslev, T., Chou, R. Y., Kroner, K. F., 1992. ARCH modeling in finance: A review of the theory and empirical evidence. Journal of Econometrics 52, 5-59.
Brailsford, T. J., Faff, R. W., 1996. An evaluation of volatility forecasting techniques. Journal of Banking and Finance 20, 419-438.
Brooks, C., Persand, G., 2002. Model choice and Value-at-Risk performance. Financial Analysts Journal 58, 87-97.
Dickey, D., Fuller, W., 1979. Distribution of the estimators for autoregressive time series with a unit root. Journal of the American Statistical Association 74, 427-431.
Diebold, F. X., Mariano, R. S., 1995. Comparing predictive accuracy. Journal of Business & Economic Statistics 13, 253-263.
Engle, R. F., 1982. Autoregressive conditional heteroskedasticity with estimates of variance of UK inflation. Econometrica 50, 987-1008.
Fama, E., 1965. The behavior of stock market prices. Journal of Business 38, 34-105.
Gonzàlez-Rivera, G., 1998. Smooth transition GARCH models. Studies in Nonlinear Dynamics & Econometrics 3, 61-78.
Hagerman, R. L., 1978. Notes: more evidence on the distribution of security returns. Journal of Finance 33, 1213-1221.
Hansen, B. E., 1994. Autoregressive conditional density estimation. International Economic Review 35, 705-730.
Hsu, D. A., Miler, R. B., Wichern, D. W., 1974. On the stable paretian behavior of stock market prices. Journal of American Statistical Association 69, 108-113.
Inoue, A., Kilian, L., 2004. In sample or out of sample tests for predictability: Which one should we use? Econometric Reviews 23, 371-402.
Jarque, C. M., Bera, A. K., 1987. A test for normality of observations and regression residuals. International Statistical Reviews 55, 163-172.
Lee, C. F., Chen, G. M., Rui, O. M., 2001. Stock returns and volatility on China stock markets. Journal of Financial Research 24, 523-543.
Lehnert, T., 2003. Explaining smiles: GARCH option pricing with conditional leptokurtosis and skewness. The Journal of Derivatives 10, 27-39.
Lopez, J., 2001. Evaluating the predictive accuracy of variance models. Journal of Forecasting 20, 87-109.
Mandelbrot, B., 1963. The variation of certain speculative prices. Journal of Business 36, 394-419.
Marcucci, J., 2005. Forecasting stock market volatility with regime-switching GARCH models. Studies in Nonlinear Dynamics & Econometrics 9, 1-53.
Markowitz, H., 1952. Portfolio selection. Journal of Finance 7, 77-91.
Mittnik, S., Paolella, M. S., 2000. Conditional density and Value-at-Risk prediction of Asian currency exchange rates. Journal of Forecasting 19, 313-333.
Nelson, D. B., 1991. Conditional heteroskedasticity in asset returns: A new approach. Econometrica 59, 347-370.
Phillips, P. C. B., Perron, P., 1988. Testing for a unit root in time series regression. Biometrika 75, 335-346.
Politis, N. D., 2004. A heavy-tailed distribution for ARCH residuals with application to volatility prediction. Annals of Economics and Finance 5, 283-298.
Sadorsky, P., 2006. Modeling and forecasting petroleum futures volatility. Energy Economics 28, 467-488.
Taylor, J. W., 2004. Volatility forecasting with smooth transition exponential smoothing. International Journal of Forecasting 20, 273-286.
Taylor, S. J., 1994. Modelling stochastic volatility: A review and comparative study. Mathematical Finance 4, 183-204.
Theodossiou, P., 2000. Skewed generalized error distribution of financial assets and option pricing. School of Business, Rutgers University, Working Paper (http://papers.ssrn.com/sol3/papers.cfm?abstract_id=219679).
Xu, J. G., 1999. Modeling Shanghai stock market volatility. Annals of Operations Research 87, 141-152.
BIBLIOGRAPHY
Angelidis, T., Benos, A., Degiannakis, S., 2004. The use of GARCH models in VaR estimation. Statistical Methodology 1, 105-128.
Bekaert, G., Erb, C., Harvey, C., Viskanta, T., 1998. Distributional characteristics of emerging market returns and asset allocation. Journal of Portfolio Management 24 (2), 102-116.
Billio, M., Pelizon, L., 2000. Value-at-Risk: A multivariate switching regime approach. Journal of Empirical Finance 7, 531-554.
Bollerslev, T., 1986. Generalized autoregressive conditional heteroskedasticity. Journal of Econometrics 31, 307-327.
Bollerslev, T., 1987. A conditionally heteroskedastic time series model for speculative prices and rates of return. Review of Economics and Statistics 69, 542-547.
Bollerslev, T., Chou, R. Y., Kroner, K. F., 1992. ARCH modeling in finance: A review of the theory and empirical evidence. Journal of Econometrics 52, 5-59.
Brooks, C., Persand, G., 2002. Model choice and Value-at-Risk performance. Financial Analysts Journal 58 (5), 87-97.
Cabedo, J. D., Moya, I., 2003. Estimating oil price ‘value at risk’ using the historical simulation approach. Energy Economics 25 (3), 239-253.
Chiu, C. L., Lee, M. C., Hung, J. C., 2005. Estimation of Value-at-Risk under jump dynamics and asymmetric information. Applied Financial Economics 15, 1095-1106.
Christoffersen, P. F., Diebold, F., 2000. How relevant is volatility forecasting for financial risk management? Review of Economics and Statistics 82 (1), 12-22.
Engel, J., Gizycki, M., 1999. Conservatism, accuracy and efficiency: Comparing Value-at-Risk models. Working Paper Series Number wp0002. Australian Prudential Regulation Authority.
Engle, R., 1982. Autoregressive conditional heteroskedasticity with estimates of variance of UK inflation. Econometrica 50, 987-1008.
Giot, P., 2000. Intraday Value-at-Risk. CORE DP 2045, Maastricht University METEOR RM/00/030.
Giot, P., Laurent, S., 2003a. Market risk in commodity markets: A VaR approach. Energy Economics 25 (5), 435-457.
Giot, P., Laurent, S., 2003b. Value-at-Risk for long and short trading positions. Journal of Applied Econometrics 18, 641-664.
Giot, P., Laurent, S., 2004. Modeling daily Value-at-Risk using realized volatility and ARCH type models. Journal of Empirical Finance 11, 379-398.
Hendricks, D., 1996. Evaluation of Value-at-Risk models using historical data. Federal Reserve Bank of New York, Economic Policy Review, April, 39-69.
Huang, Y. C., Lin, B. J., 2004. Value-at-Risk analysis for Taiwan stock index futures: Fat tails and conditional asymmetries in return innovations. Review of Quantitative Finance and Accounting 22, 79-95.
Jarque, C. M., Bera, A. K., 1987. A test for normality of observations and regression residuals. International Statistics Review 55, 163-172.
Jones, C., Kaul, G., 1996. Oil and the stock markets. Journal of Finance 51, 463-491.
Jorion, P., 2000. Value at Risk: The new benchmark for managing financial risk. McGraw-Hill, New York.
Kupiec, P., 1995. Techniques for verifying the accuracy of risk management models. The Journal of Derivatives 3, 73-84.
Lopez, J., 1999. Methods for evaluating Value-at-Risk estimates. Federal Reserve Bank of San Francisco, Economic Review 2, 3-17.
Politis, N. D., 2004. A heavy-tailed distribution for ARCH residuals with application to volatility prediction. Annals of Economics and Finance 5, 283-298.
Sadorsky, P., 1999. Oil price shocks and stock market activity. Energy Economics 21 (5), 449-469.
Sadorsky, P., 2003. The macroeconomic determinants of technology stock price volatility. Review of Financial Economics 12, 191-205.
Sadorsky, P., 2006. Modeling and forecasting petroleum futures volatility. Energy Economics 28 (4), 467-488.
So, M. K. P., Yu, P. L. H., 2006. Empirical analysis of GARCH models in Value at Risk estimation. International Financial Markets, Institutions & Money 16, 180-197.
van den Goorbergh, R. W. J., Vlaar, P. J. G., 1999. Value-at-Risk analysis of stock returns: Historical simulation, variance techniques or tail index estimation? De Nederlandsche Bank, DNB Staff Reports 40.
BIBLIOGRAPHY
Akgiray, V., 1989. Conditional heteroskedasticity in time series of stock return: Evidence and forecasts. Journal of Business 62, 55-80.
Ané, T., 2006. An analysis of the flexibility of asymmetric power GARCH models. Computational Statistics & Data Analysis 51, 1293-1311.
Angelidis, T., Benos, A., Degiannakis, S., 2004. The use of GARCH models in VaR estimation. Statistical Methodology 1, 105-128.
Bali, T. G., Theodossiou, P., 2007. A conditional-SGT-VaR approach with alternative GARCH models. Annals of Operations Research 151, 241-267.
Bams, D., Lehnert, T., Wolff, C. P., 2005. An evaluation framework for alternative VaR-models. Journal of International Money and Finance 24, 944-958.
Bollerslev, T., Chou, R. Y., Kroner, K. F., 1992. ARCH modeling in finance: A review of the theory and empirical evidence. Journal of Econometrics 52, 5-59.
Bollerslev, T., Wooldridge, J., 1992. Quasi-maximum likelihood estimation and inference in dynamic models with time-varying covariances. Econometric Reviews 11, 143-172.
Brooks, C., Persand, G., 2003. The effect of asymmetries on stock index return Value-at-Risk estimates. Journal of Risk Finance 4, 29-42.
Cabedo, J. D., Moya, I., 2003. Estimating oil price ‘value at risk’ using the historical simulation approach. Energy Economics 25 (3), 239-253.
Christoffersen, P. F., 1998. Evaluating interval forecasts. International Economic Review 39, 841-862.
Dickey, D., Fuller, W., 1979. Distribution of the estimators for autoregressive time series with a unit root. Journal of the American Statistical Association 74, 427-431.
Diebold, F. X., Mariano, R. S., 1995. Comparing predictive accuracy. Journal of Business & Economic Statistics 13, 253-263.
Giot, P., Laurent, S., 2003a. Value-at-Risk for long and short trading positions. Journal of Applied Econometrics 18, 641-664.
Giot, P., Laurent, S., 2003b. Market risk in commodity markets: A VaR approach. Energy Economics 25 (5), 435-457.
Giot, P., Laurent, S., 2004. Modeling daily Value-at-Risk using realized volatility and ARCH type models. Journal of Empirical Finance 11, 379-398.
Huang, Y. C., Lin, B. J., 2004. Value-at-Risk analysis for Taiwan stock index futures: Fat tails and conditional asymmetries in return innovations. Review of Quantitative Finance and Accounting 22, 79-95.
Hung, J. C., Lee, M. C., Liu, H. C., 2008. Estimation of Value-at-Risk for energy commodities via fat-tailed GARCH models. Energy Economics 30(3), 1173-1191.
Jarque, C. M., Bera, A. K., 1987. A test for normality of observations and regression residuals. International Statistics Review 55, 163-172.
Jorion, P., 2000. Value at Risk: The new benchmark for managing financial risk. McGraw-Hill, New York.
Kupiec, P., 1995. Techniques for verifying the accuracy of risk management models. The Journal of Derivatives 3, 73-84.
Lambert, P, Laurent, S., 2001. Modelling financial time series using GARCH-type models and a skewed student density, Mimeo, Université de Liegè.
Lee, M. C., Su, J. B., Liu, H. C., 2008. Value-at-Risk in US stock indices with skewed generalized error distribution. Applied Financial Economics Letters, 1-7 (in press).
Lin, C. H., Shen, S. S., 2006. Can the student-t distribution provide accurate value at Risk? Journal of Risk Finance 7, 292-300.
Lopez, J., 1999. Methods for evaluating Value-at-Risk estimates. Federal Reserve Bank of San Francisco, Economic Review 2, 3-17.
Marcucci, J., 2005. Forecasting stock market volatility with regime-switching GARCH models. Studies in Nonlinear Dynamics & Econometrics 9, 1-53.
Mittnik, S., Paolella, M. S., Rachev, S. T., 2000. Diagnosing and treating the fat tails in financial return data. Journal of Empirical Finance 7, 389-416.
Phillips, P. C. B., Perron, P., 1988. Testing for a unit root in time series regression. Biometrika 75, 335-346.
Sadeghi, M., Shavvalpour, S., 2006. Energy risk management and Value at Risk modeling. Energy Policy 34, 3367-3373.
Sadorsky, P., 2006. Modeling and forecasting petroleum futures volatility. Energy Economics 28 (4), 467-488.
Sarma, M., Thomas, S., Shah, A., 2003. Selection of Value-at-Risk models. Journal of Forecasting 22, 337-358.
So, M. K. P., Yu, P. L. H., 2006. Empirical analysis of GARCH models in Value at Risk estimation. International Financial Markets, Institutions & Money 16, 180-197.
Su, E., Knowles, T. W., 2006. Asian pacific stock market volatility modeling and Value at Risk analysis. Emerging Markets Finance and Trade 42, 18-62.
Theodossiou, P., 1998. Financial data and the skewed generalized t distribution. Management Science 44, 1650-1661.
Wu, P. T., Shieh, S. J., 2007. Value-at-Risk analysis for long-term interest rate futures: Fat-tail and long memory in return innovations. Journal of Empirical Finance 14, 248-259.
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