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System No. U0002-2706201210380700
Title (in Chinese) 動態價格跳躍與最小變異數避險組合的預期不足額:以西德州原油與期貨價格為例
Title (in English) Dynamic Price Jump and the Expected Shortfall of Minimum Variance Hedging Portfolio : The Case of WTI Crude Oil and Futures Prices
Other Title
Institution 淡江大學
Department (in Chinese) 管理科學學系碩士班
Department (in English) Master’s Program, Department of Management Sciences
Other Division
Other Division Name
Other Department/Institution
Academic Year 100
Semester 2
PublicationYear 101
Author's name (in Chinese) 劉人豪
Author's name(in English) Jen-Hau Liu
Student ID 697620028
Degree 碩士
Language Traditional Chinese
Other Language
Date of Oral Defense 2012-06-22
Pagination 29page
Committee Member advisor - Chung-Chu Chuang
advisor - Yi-Hsien Wang
co-chair - Kuo-Ren Lou
co-chair - Chung-Gee Lin
co-chair - Hui-Chen Chiang
Keyword (inChinese) 期貨
Keyword (in English) Futures
Expected Shortfall
Value at Risk
bivariate ARJI model
minimum variance hedging portfolio
Other Keywords
Abstract (in Chinese)
原油價格波動受國際政經影響甚劇,針對原油價格波動進行風險管理已成為投資人的主要課題。由於原油價格與期貨價格可能皆會因稀少事件的發生而存著價格不連續現象。本研究先利用Chan and Young (2006) 提出的雙變量ARJI-GARCH模型捕捉價格不連續的變動及現貨報酬與期貨報酬的共變異數關係。以2010年至2011年美國西德州原油價格為主要研究對象,利用移動視窗(rolling window)法探討樣本外(out of sample)預期不足額,比較未避險模型、雙變量GARCH模型與雙變量ARJI-GARCH模型的最小變異數避險組合之條件預期不足額。研究發現因雙變量ARJI-GARCH模型能捕捉資產間動態波動性、跳躍動態過程與相關跳躍關係,因此估計最小變異數避險組合的條件預期不足額,比起未避險模型與雙變量GARCH模型,有較佳的表現。因此,若僅考慮資產價格間的動態波動性,容易造成投資人承擔超過預期的損失,此結果可為投資人避險的參考。
Abstract (in English)
The fluctuations of the crude oil prices were severely influenced by the international political and economic influence. For the crude oil price volatility, risk management has become the main topics of the investors. For some rare events, the crude oil spot and futures prices are likely to maintain the phenomenon of price jump. In this study, the change of the price jump and the covariance relations of the spot and futures returns are captured by the bivariate ARJI-GARCH model proposed by Chan and Young (2006). The main research object is the spot and futures price of U.S. West Texas Intermediate crude oil in 2010-2011. Using the rolling-window method estimates the out-of-sample expected shortfall. The conditional expected shortfall of the minimum variance hedge portfolio is estimated by three models, unhedge model(GARCH model), bivariate GARCH model and bivariate ARJI-GARCH model. By comparing the estimating results, this study found that the bivariate ARJI-GARCH model estimates the conditional expected shortfall of the minimum variance hedge portfolio owns a better performance, because the bivariate ARJI-GARCH model can capture the dynamic volatility, dynamic jump process and the jump relation between the assets. Therefore, if considering only the dynamic volatility of asset prices, investors will be likely to bear the loss more than expected. This results can be a reference for investors to hedge.
Other Abstract
Table of Content (with Page Number)
目錄	I
表目錄	II
圖目錄	III
1. 緒論	1
1.1 研究背景與動機	1
1.2 研究目的	5
2. 資料與方法	6
2.1 樣本與資料來源	6
2.2 實證模型	6
2.3 最小變異數避險比率	9
2.4 最小條件變異數避險組合的條件風險值與條件預期不足額	10
3. 實證結果分析	13
3.1 基本敘述統計分析	13
3.2 單根檢定分析	15
3.3 模型估計參數	15
3.4 最小變異數平均避險比率	19
3.5 最小變異數避險組合的條件預期不足額之衡量與分析	19
4. 結論與建議	23
4.1 結論	23
4.2 建議	24
參考文獻	25
表 3-1 自然對數報酬的基本敘述統計量分析	14
表 3-2 ADF、PP和KPSS 檢定	15
表 3-3 模型的參數估計與檢定	17
表 3-4 最小變異數避險組合的避險比率	19
表 3-5 最校變異數避險組合的條件風險值	19
表 3-6 最小變異數避險組合的條件預期不足額	20
表 3-7 條件預期不足額的檢定	21
圖 3-1 西德州原油現貨與期貨日價格與日報酬時間走勢圖	13
圖 3-2 移動視窗法架構	16
1.	Acerbi, C. and D. Tasche, (2002), On the Coherence of Expected Shortfall. Journal of Banking and Finance, Vol. 26, No. 7, pp. 1487-1503.
2.	Artzner, P., F. Delbaen, J. M. Eber, and D. Heath, (1997), Thinking Coherently, Risk, Vol. 10, No. 11, pp. 68-71.
3.	Artzner, P., F. Delbaen, J. M. Eber, and D. Heath, (1999), Coherent Measures of Risk, Mathematical Finance, Vol. 9, No. 3, pp. 203-228.
4.	Benet, B. A., (1992), Hedging Period Length and Ex-Ante Futures Hedging Effectiveness: The Cases of Foreign Exchange Risk Cross Hedges. Journal of Futures Markets, Vol. 12, No. 2, pp. 163-175.
5.	Benito, F., A. Leon and J. Nave, (2007), Modeling the Euro Overnight Rate. Journal of Empirical Finance, Vol. 14, No. 5, pp. 756-782.
6.	Bollerslev, T., (1986), Generalized Autoregressive Conditional Heterosce - dasticity. Joural of Econometrices, Vol. 31, pp. 307-327.
7.	Chan, W. H., (2008), Dynamic Hedging with Foreign Currency Futures in the Presence of Jumps. Studies in Nonlinear Dynamics & Econometrics, Vol. 12, No. 2, pp. 1558-3708.
8.	Chan, W. H. and J. M. Maheu, (2002), Conditional Jump Dynamics in Stock Market Returns. Journal of Business and Economic Statistics, Vol. 20, No. 3, pp. 377-389.
9.	Chan, W. H. and D. Young, (2006), Jumping Hedges: An Examination of Movements in Copper Spot and Futures Markets. Journal of Futures Markets, Vol. 26, No. 2, pp. 169-188.
10.	Chang, T. H., H. M. Su and C. L. Chiu, (2010), Value-at-Risk Estimation with the Optimal Dynamic Biofuel Portfolio. Energy Economics, Vol. 33, No. 2, pp. 264-272.
11.	Chang, K. L., (2011), The Optimal Value-at-Risk Hedging Dtrategy Under Bivariate Regime Switching ARCH Framework. Applied Economics, Vol. 43, No. 21, pp. 2627-2640.
12.	Chang, C.L., M. McAleer and R. Tansuchat, (2011), Crude Oil Hedging Strategies Using Dynamic Multivariate GARCH. Energy Economics, Vol. 33, No. 5, pp. 912-923.
13.	Cheng, W. H. and J. C. Hung, (2011), Skewness and Leptokurtosis in GARCH-Typed VaR Estimation of Petroleum and Metal Asset Returns. Journal of Empirical Finance, Vol. 18, No. 1, pp. 160-173.
14.	Chung, S. K., (2009), Bivariate Mixed Normal GARCH Models and Out-of-Sample Hedge Performances. Finance Research Letters, Vol 6, No. 3, pp. 130-137.
15.	Das, S. R. and R. K. Sundaram, (1997), Taming the Skew: Higher-Order Moments in Modeling Asset Price Processes in Finance. National Bureau of Economic Research, Working Paper 5976.
16.	Duffie, D. and J. Pan, (1997), An Overview of Value at Risk. Journal of Derivatives, Vol. 4, No. 3, pp. 7-49.
17.	Engle, R. F., (1982), Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation. Econometrica, Vol. 50, No. 4, pp. 987-1007.
18.	Engle, R. F. and K. F. Kroner, (1995), Multivariate Simultaneous Generalized ARCH. Econometric Theory, Vol. 11, No. 1, pp.122-150.
19.	Hammoudeh, S., F. Malik and M. McAleer, (2011), Risk Management of Precious Metals. Quarterly Review of Economics and Finance, Vol. 51, No. 4, pp. 435–441.
20.	Huang, J. J., K. J. Lee, H. Liang and W. F. Lin, (2009), Estimating Value at Risk of Portfolio by Conditional Copula-GARCH Method.  Insurance: Mathematics and Economics, Vol. 45, No. 3, pp. 315–324.
21.	Hung, J. C., C. L. Chiu and M. C. Lee, (2006), Hedging with Zero-Value at Risk Hedge Ratio. Applied Financial Economics, Vol. 16, No. 3, pp. 259-269.
22.	Hlouskova, J., K. Schmidheiny and M. Wagner, (2009), Multistep Predictions for Multivariate GARCH Models: Closed Form Solution and the Value for Portfolio Management. Journal of Empirical Finance, Vol. 16, No. 2, pp. 330-336.
23.	Jarque, C.M. and A.K. Bera, (1987), A Test for Normality of Observations and Regression Residuals, International Statistical Review, Vol. 55, No. 2, pp. 163–172.
24.	Johnson, L., (1960), The Theory of Hedging and Speculation in Commodity Futures. Review of Economic Studies, Vol. 27, No. 3, pp.139-151.
25.	Kwiatkowski, D., P. C. B. Phillips, P. Schmidt and Y. Shin, (1992), Testing the Null Hypothesis of Stationarity Against the Alternative of a Unit Root: How Sure Are We that Economic Time Series Have a Unit Root? Journal of Econometrics, Vol. 54, No. 1-3, pp. 159-178.
26.	Lee, M. C., C. L. Chiu and Y. H. Lee, (2007), Is Twin Behavior of Nikkei 225 Index Futures the Same? Physica A: Statistical Mechanics and Its Applications, Vol. 377, No. 1, pp. 199-210.
27.	Lin, S. X. and M. N. Tamvakis, (2001), Spillovereffects in Energy Futures Markets. Energy Economics, Vol. 23, No. 1, pp. 43-56.
28.	Lin, C. M., Y. H. Lee and C. L. Chiu, (2009), Structural Changes in Foreign investors’ Trading Behavior and the Corresponding Impact on Taiwan's Stock Market. Research in International Business and Finance, Vol. 23, No. 1, pp. 78-89.
29.	Mabrouk, S. and S. Saadi, (2012), Parametric Value-at-Risk Analysis: Evidence from Stock Indices. Quarterly Review of Economics and Finance, (Forthcoming), from Website: http://www.sciencedirect.com/science/article/pii/S1062976912000294
30.	Maner, M., A. Lanza and M. McAleer, (2006), Modeling Dynamic Conditional Correlations in WTI Oil Forward and Futures Returns. Finance Research Letters, Vol. 3, No. 2, pp. 114-132.
31.	Milunovich, G. and S. Thorp, (2006), Valuing Volatility Spillovers. Global Finance Journal, Vol. 17, No. 1, pp. 1-22.
32.	Morgan, I. G., (1976), Stock Prices and Heteroscedasticity, Journal of Business, Vol. 49, No. 4, pp. 496-508.
33.	Park, S. Y. and S. Y. Jei, (2009), Estimation and Hedging Effectiveness of Time-Varying Hedge Ratio: Flexible Bivariate Garch Approaches. Journal of Futures Markets, Vol. 30, No. 1, pp. 71-99.
34.	Phillips, P. C. B. and P. Perron, (1988), Testing for Unit in Time Series Regression. Biometrika, Vol. 75, No. 2, pp. 335-346.
35.	Pok, W. C., S. S. Poshakwale and J. L. Ford, (2009), Stock Index Futures Hedging in the Emerging Malaysian Market. Global Finance Journal, Vol. 20, No. 3, pp. 273-288.
36.	Said, S.E. and D.A. Dickey, (1984), Testing for Unit Roots in Autoregressive Moving Average Models of Unknown Order. Biometrika, Vol. 71, No. 3, pp. 599-607.
37.	Stavroyiannis, S., I. Makris, V. Nikolaidis and L. Zarangas, (2012), Econometric Modeling and Value-at-Risk Using the Pearson Type-IV Distribution. International Review of Financial Analysis, Vol. 22, pp. 10-17. (Forthcoming), from Website: http://www.sciencedirect.com/science/article/pii/S105752191200018X
38.	Su, J. B. and J. C. Hung, (2010), Empirical Analysis of Jump Dynamics, Heavy-Tails and Skewness on Value-at-Risk Estimation. Economic Modelling, Vol. 28, No. 3, pp. 1117–1130.
39.	Wang, Y., C. F. Wu and Y. Wei, (2011), Can GARCH-Class Models Capture Long Memory in WTI Crude Oil Markets? Economic Modelling, Vol. 28, No. 3, pp. 921-927.
40.	Working, H., (1953), Futures Trading and Hedging. American Economic Review, Vol. 4, No. 3, pp. 314-34.
41.	Yamai, Y. and T. Yoshiba, (2005), Value-at-Risk Versus Expected Shortfall: a Practical Perspective. Journal of Banking and Finance, Vol. 29, No. 4, pp. 997–1015.
42.	Zhu, D. and J. W. Galbraith, (2011), Modeling and Forecasting Expected Shortfall with the Generalized Asymmetric Student-t and Asymmetric Exponential Power Distributions. Journal of Empirical Finance, Vol 18, No. 4, pp. 765-778.
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