全球對能源需求殷切，原油為經濟活動中的重要資源之一。原油報酬的波動性叢聚、厚尾與極端事件易產生尾部關聯結構改變，因而避險常成為避險者的重要課題之一。本研究以1986年1月2日至2018年02月28日的西德州原油現貨與期貨為研究標的，在移動視窗架構與GARCH-EVT-Copula模型下，探討原油現貨與原油期貨的避險組合不同分配的最小變異數的避險績效。本研究發現常態分配與t分配的GARCH-EVT-Copula模型的最小變異數避險組合的避險績效無顯著差異。然而，波斯灣戰爭前與金融海嘯後的兩模型最小變異數避險組合的避險績效有顯著差異，本研究結果可做為投資人避險的參考。

The global market has a large demand of energy. Crude oil is one of important resources in economic activities. Because crude oil returns exists volatility clustering, fat-tail and dependence structure changes of tail behavior from extreme events, hedging plays an important role for producers. The study examined West Texas Intermediate crude oil spot and futures. The rolling-window method is used to study the hedging portfolio of West Texas Intermediate crude oil spot and futures by using GARCH-EVT-Copula model. Then, Comparing Normal distribution with Student-t distribution. The empirical results show that both hedging effectiveness of t distribution and Normal distribution don’t have significant difference. However, there are significant differences in the hedging performance of two models for the minimum variance hedging portfolio before the Persian Gulf War and after the financial crisis. These findings in this study can be used as a reference for investors.

目錄
目錄	I
圖目錄	II
表目錄	III
第一章　緒論	1
1.1 研究背景與動機	1
1.2 研究目的	8
1.3 研究範圍	8
1.4 研究架構	9
第二章　樣本與實證模型	11
2.1 樣本與資料來源	11
2.2 實證模型	11
第三章　原油現貨與期貨的避險績效實證結果分析	20
3.1 基本敘述統計量分析	20
3.2 單根檢定	23
3.3 極值分析	27
3.4 實證模型參數估計與檢定	28
3.5 西德州原油現貨與期貨的最小變異數避險組合的避險績效分析	31
第四章　結論與建議	36
4.1 結論	36
4.2 建議	36
參考文獻	38

圖目錄

圖1-1 研究流程	10
圖3-1 西德州原油現貨與期貨價格走勢圖	21
圖3-2 西德州原油現貨與期貨報酬走勢圖	21
圖3-3現貨與期貨報酬的常態Q-Q圖	27
圖3-4 移動視窗架構圖	28

表目錄
表3-1  日報酬基本敘述統計量	23
表3-2  ADF檢定	24
表3-3  PP檢定	25
表3-4  KPSS檢定	26
表3-5  GJR-GARCH參數估計與檢定	29
表3-6  GPD模型的參數估計與檢定	30
表3-7  Copula模型的參數估計與檢定	31
表3-8  最小變異數避險比率	31
表3-9  最小變異數避險績效的比較	32
表3-10 重大事件的最小變異數避險比率	33
表3-11 重大事件的最小變異數避險績效	34
表3-12 重大事件的最小變異數避險績效的比較	35

1. Aloui, R., Aissa, M. S. B., & Nguyen, D. K. (2013). “Conditional dependence structure between oil prices and exchange rates: A COPULA-GARCH approach.” Journal of International Money and Finance. 32, pp.719-738.
2. Angham, B. B., Sebai, S., & Naoui, K. (2015). “A study of the interactive relationship between oil price and exchange rate: A copula approach and a DCC-MGARCH model.” Journal of Economic Asymmetries. 12(2), pp.173-189.
3. Barbi, M., & Romagnoli, S. (2013). “A COPULA‐based quantile risk measure approach to estimate the optimal hedge ratio.” Journal of Futures Markets. 34(7), pp.658-675.
4. Bhattacharyyaa, M., & Ritoliab, G. (2008). “Conditional VaR using EVT – Towards a planned margin scheme.” International Review of Financial Analysis. 17(2), pp.382-395.
5. Bollerslevab, T. (1986). “Generalized autoregressive conditional heteroskedasticity.” Journal of Econometrics. 31(3), pp.307-327.
6. Byström, H. N. E. (2004). “Managing extreme risks in tranquil and volatile markets using conditional extreme value theory.” International Review of Financial Analysis. 13(2), pp.133-152.
7. Chang, C. Y., Lai, J. Y., & Chuang, I. Y. (2010). “Futures hedging effectiveness under the segmentation of bear/bull energy markets.” Energy Economics. 32(2), pp.442-449.
8. Chang, C. L., McAleer, M., & Tansuchat, R. (2011). “Crude oil hedging strategies using dynamic multivariate GARCH.” Energy Economics. 33(5), pp.912-923.
9. Chau, F., Deesomsak, R., & Wang, J. (2014). “Political uncertainty and stock market volatility in the Middle East and North African (MENA) countries.” Journal of International Financial Markets, Institutions and Money. 28, pp.1-19.
10. Chen, W. C., Liu, K. P., Yang, Y. L., & Lai, Y. H. (2014). “Dynamic hedging in stock index futures via Copula multiplicative error model.” Journal of Applied Economics Letters, 21(12), pp.801-805.
11. Creti, A., Joëts, M., & Mignon, V. (2013). “On the links between stock and commodity markets' volatility.” Energy Economics. 37, pp.16-28.
12. Engle, R. F. (1982). “Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation.” Econometrica. 50(4), pp.987-1007.
13. Engle, R. F., & Ng, V. K. (1993). “Measuring and testing the impact of news on volatility.” Journal of Finance. 48(5), pp.1749-1778.
14. Glosten, L. R., Jagannathan, R., & Runkle D. E., (1993). “On the relation between the expected value and the volatility of the nominal excess return on stocks.” Journal of Finance. 48(5), pp.1779-1801.
15. Goorbergh, R. V. D. (2004). “A COPULA-based autoregressive conditional dependence model of international stock markets.” Insurance: Mathematics and Economics. 37(1), pp.101-114.
16. Gou, H., Chen, X., & Hua, Y. (2015). “Measuring the value at risk of foreign exchange portfolio by a GARCH-EVT-COPULA based model.” Journal of Industrial Engineering and Engineering Management. 29(1), pp.183-193.
17. Henze, N., & Zirkler, B. (1990). “A class of invariant consistent tests for multivariate normality.” Communications in Statistics: Theory and Methods. 19, 3595- 3618.
18. Huang, J. J., Lee, K. J., Liang, H. M., & Lin, W. F. (2009). “Estimating value at risk of portfolio by conditional COPULA-GARCH method.” Insurance: Mathematics and Economics. 45(3), pp.315-324.
19. Jarque, C. M., & Bera, A. K. (1980). “Efficient tests for normality, homoscedasticity and serial independence of regression residuals.” Economics letters. 6(3), pp.255-259.
20. Kankainen, A., Taskinen, S., & Oja, H. (2007). “Tests of multinormality based on location vectors and scatter matrices.” Statistical Methods and Applications. 16(3), pp.357-379.
21. Karmakar, M. (2017). “Dependence structure and portfolio risk in Indian foreign exchange market: A GARCH-EVT- COPULA approach.” Quarterly Review of Economics and Finance. 64, pp.275-291.
22. Khemawanit, K., & Tansuchat, R. (2016). “The analysis of value at risk for precious metal returns by applying extreme value theory, Copula model and GARCH model.” International Journal of Applied Business and Economic Research. 24(2), pp.1011-1025.
23. Kim, J. M., & Jung, H. (2016). “Linear time-varying regression with COPULA–DCC–GARCH models for volatility.” Economics Letters. 145, pp.262-265.
24. Kim, S. C., Park, C. H., & Yun, Y. J. (2014). “Hedging with mini gold futures: Evidence from Korea.” Eurasian Economic Review. 4(2), pp.163-176.
25. Lai, Y. H., Chen, C. W. S., & Gerlach, R. (2009). “Optimal dynamic hedging via COPULA-THRESHOLD-GARCH models.” Mathematics and Computers in Simulation. 79(8), pp.2609-2624.
26. Login, F. M. (2000). “From value at risk to stress testing: The extreme value approach.” Journal of Banking & Finance. 24(7), pp1097-1130.
27. Lin, B., Wesseh, P. K., & Appiah, M O. (2014). “Oil price fluctuation, volatility spillover and the Ghanaian equity market: Implication for portfolio management and hedging effectiveness.” Energy Economics. 42, pp.172-182.
28. Liu, H. C., & Hung, J. C. (2010). “Forecasting S&P-100 stock index volatility: The role of volatility asymmetry and distributional assumption in GARCH models.” Expert Systems with Applications. 37(7), pp.4928-4934.
29. McNeil, A. J. (1998). “Calculating quantile risk measures for financial return series using extreme value theory.” ETH Zurich. 
30. McNeil, A. J., & Frey, R. (2000). “Estimation of tail-related risk measures for heteroscedastic financial time series: An extreme value approach.” Journal of Empirical Finance. 7(3-4), pp.271-300.
31. Mensi, W., Hammoudeh, S., Shahzad, S. J. H., & Shahbaz, M. (2017). “Modeling systemic risk and dependence structure between oil and stock markets using a variational mode decomposition-based copula method.” Journal of Banking & Finance. 75, pp.258-279.
32. Mokni, K., & Mansouri, F. (2017). “Conditional dependence between international stock markets: A long memory GARCH- COPULA model approach.” Journal of Multinational Financial Management. 42-43, pp.116-131.
33. Nawaz, F., & Qayyum, A. (2012). “Value-at-Risk and extreme value distribution for financial returns of Pakistani firms.” Journal of Basic and Applied Scientific Research, 2(8), pp.7454-7458.
34. Reboredo, J. C. (2011). “How do crude oil prices co-move?: A copula approach.” Energy Economics. 33(5), pp.948-955.
35. Reboredo, J. C. (2013). “Is gold a safe haven or a hedge for the US dollar? Implications for risk management.” Journal of Banking & Finance. 37(8), pp.2665-2676.
36. Ren, F., & Giles, D. E. (2010). “Extreme value analysis of daily Canadian crude oil prices.” Journal of Applied Financial Economics. 20(12), pp.941-954.
37. Ripple, R. D., & Moosa, I. A. (2007). “Hedging effectiveness and futures contract maturity: The case of NYMEX crude oil futures.” Journal of Applied Financial Economics. 17(9), pp.683-689.
38. Sahamkhadam, M., Stephan, A., & Östermark, R. (2018). “Portfolio optimization based on GARCH-EVT-COPULA forecasting models.” International Journal of Forecasting, 34(3), pp.497-506.
39. Sklar, A. (1959), “Fonctions de repartition an dimensions et leurs marges”. Publications Inst. Statis. Univ. Paris. 8, pp.229-231.
40. Su, Y. C., Huang, H. C., & Lin, Y. J. (2011). “GJR-GARCH model in value-at-risk of financial holdings.” Journal of Applied Financial Economics. 24, pp.1819-1829.
41. Switzer, L. N., & El‐Khoury, M. (2006). “Extreme volatility, speculative efficiency, and the hedging effectiveness of the oil futures markets.” Journal of Futures Markets. 27(1), pp.61-84.
42. Teterin, P., Brooks, R., & Enders, W. (2016). “Smooth volatility shifts and spillovers in U.S. crude oil and corn futures markets.” Journal of Empirical Finance. 38, pp.22-36.
43. Wang, Z. R., Chen, X. H., & Zhou, Y. J. (2010). “Estimating risk of 
foreign exchange portfolio: Using VaR and CVaR based on 
GARCH–EVT-COPULA model.” Physica A: Statistical Mechanics and its Applications. 389(21), pp. 4918-4928.
44. Wei, Y., Wang, Y. D., & Huang, D. S. (2011). “A COPULA–multifractal volatility hedging model for CSI 300 index futures.” Physica A: Statistical Mechanics and its Applications. 390(23-24), pp. 4260-4272.
45. Youssef, M., Belkacem, L., & Mokni, K. (2015). “Value-at-Risk estimation of energy commodities: A long-memory GARCH–EVT approach.” Energy Economics. 51, pp.99-110.
46. Yun, W. C., & Kim, H. J. (2010). “Hedging strategy for crude oil trading and the factors influencing hedging effectiveness.” Energy Policy. 38(5), pp.2404-2408.