臺灣博碩士論文加值系統

東吳大學93學年度第二學期碩士學位論文
論文題目：台灣十年期公債期現貨市場關聯性及避險比率與績效之實證研究—VEC-TGARCH模式之應用
所組別：經濟學系（所） （學號:90751014）
研究生：曾明欽
指導教授：劉祥熹 博士
論文提要內容：
本文利用簡單避險模型、傳統迴歸模型、誤差修正模型、單變量GARCH(1,1)模型、雙變量GARCH(1,1)模型與雙變量T-GARCH(1,1)模型等研究十年期公債期貨與現貨間之關聯性與避險效果，並比較各種避險模型之避險效益。根據實證結果發現：
一、公債期貨與現貨之時間序列資料均非穩定序列並呈非常態分配，經一階差分後兩序列即呈穩定。
二、公債期貨與現貨間存在共整合關係，即表示兩者間存在長期均衡關係。因此應將誤差修正模型納入模型中，才能使兩變數之短期動態關係不會偏離長期均衡太多。該項長期均衡關係能確保期貨與現貨價格之因果關係存在。
三、實證結果發現期貨與現貨序列皆存在波動群聚與不對稱現象，顯示探討期貨與現貨關聯性，宜納入波動群聚與不對稱效果檢定。
四、依據VECM、VECM-GARCH及VECM-TGARCH模型實證估計結果發現，期現貨互為因果關係；VECM、ECM-GARCH及VECM-GARCH模型實證估計結果顯示現貨報酬皆顯著受期貨報酬前一期之影響較大；VECM-TGARCH模型實證估計結果顯示現貨報酬皆顯著受期貨報酬前一、二期之影響較大。綜合前述，代表期貨領先現貨，期貨具價格發現功能。
五、樣本內實證發現，VECM-TGARCH模型在避險效益上最佳，VECM-GARCH模型次之，簡單避險模型之效益最差（無避險效果）。此可能是台灣公債期貨市場為剛起步階段，較不具市場效率所致。
六、樣本外實證發現，亦以VECM-TGARCH模型在避險效益上最佳，VECM- GARCH模型次之，OLS及簡單避險模型之效益較差。此狀況與前述樣本內避險之研究結果大致相同，可能是台灣公債期貨市場正處於剛起步階段，且交易較不活絡，因而較不具市場效率所致。
七、經由實證顯示，公債期貨與現貨間確實存有長期均衡關係，且期貨具有價格發現與避險功能。
Keyword: Hedge Ratio, Hedging Performance, Unit Root Test, GARCH Model

ABSTRACT
An Empirical Study on the Mutual Relationships, Hedge Ratio and Effectiveness in Taiwan 10-year government bond Futures and spot Markets ：
The Application of VEC-TGARCH Models
by
Ming-Chin Tseng
june 2005
Advisor：Dr. Hsiang-Hsi Liu
Department：Graduate Instittute of Economics
Major：Finance Management
Degree：Master of Business Administration
The purpose of this study is to examine the predicable models to generate optimal hedge ratio, and to find relationships of futures and spot. The traditional model and time-varying model have been compared in this thesis. Naïve model , OLS model , VECM model and GARCH models are involved too. The empirical data including TAIFEX Taiwan 10-year government bond futures. Data are used in this study which covered daily from Jan. 23 2004 to Mar. 29 2005. The hedging performance also has been measured by the decreasing degree of portfolio variance. The major empirical results are as follows：
1.By using unit roots testing for price series of 10-year government bond futures, it found that the significance of unit roots and thus the nonstationarity of the price series. Hence, price series should be differenced to induce stationary.
2.The result of cointegration test has shown that there is a long-run equilibrium relationships between spot and futures prices. Consequently, a cointegration measure should be taken into account in the hedge model.
3.The evidence for the effect of the volatility clustering and volatility asymmetry have been displayed in the price series. It should discuss the volatility asymmetry when the relationship between futures prices and spot prices are discussed.
4.By using VEC, VEC-GARCH and VEC-TGARCH models estimating for price series of 10-year government bond futures and spots, it found that the relationships of mutually feedback. By using VEC, EC-GARCH and VEC-GARCH models, it found that the spot prices to be effected significantly in lag 1 of the futures prices. By using VEC-TGARCH model, it found the spot price to be effected significantly in lag 1 and lag 2 of the futures prices.
5.In detecting the effects of in-of sample periods, the VEC-TGARCH model performs more well than all other hedging models for 10-year government bond futures, and the VEC-GARCH model is the second best. The results also has indicated that the hedge performance from those more complicate model is superior to those obtained from the traditional method. It shows that the history of Taiwan government bond future market maybe shorter, so the market is less effective.
6.In detecting the effects of out-of sample periods, the results also has indicated the same of the point 5.
7.In general, the findings of this study indicate that there is a long-run equilibrium relationships between spot and futures prices. They can effectively reduce there risk of investment portfolio and discover the prices of spot.

Keyword: Hedge Ratio, Hedging Performance, Unit Root Test, GARCH Model.

目 錄
第一章 緒論---------------------------------------------1
第一節 研究背景與動機---------------------------------1
第二節 研究目的---------------------------------------2
第三節 研究方法與步驟---------------------------------3
第四節 研究對象與資料來源-----------------------------4
第五節 章節架構---------------------------------------5
第二章 理論基礎與文獻回顧-------------------------------9
第一節 理論基礎---------------------------------------9
第二節 文獻回顧--------------------------------------25
第三節 本章綜論--------------------------------------38
第三章 相關計量方法與實證模型--------------------------39
第一節 定態序列與單根檢定----------------------------39
第二節 共整合、誤差修正模型及因果關係檢定模型--------45
第三節 GARCH模型之估計與檢定方法--------------------53
第四節 實證引用模型之建構----------------------------64
第五節 避險績效之衡量--------------------------------70
第四章 實證結果與分析----------------------------------73
第一節 資料描述--------------------------------------73
第二節 模式檢定結果分析------------------------------80
第三節 模型實證結果分析------------------------------89
第五章 結論與建議-------------------------------------108
第一節 結論-----------------------------------------108
第二節 建議與未來研究方向---------------------------109
參考文獻--------------------------------------------111













表 次
表1-1 台灣期貨交易所十年期利率期貨契約規格--------------7
表1-2 十年期公債期貨可交割債券暨轉換因子表--------------8
表4-1 公債期貨與現貨原始數列敘述統計表-----------------77
表4-2 公債期貨與現貨價格取對數敘述統計表---------------78
表4-3 公債期貨與現貨報酬敘述統計表---------------------79
表4-4 ADF與PP檢定結果---------------------------------82
表4-5 公債期貨最適落後期數選取-------------------------82
表4-6 公債現貨最適落後期數選取-------------------------83
表4-7 AIC準則選取最適落後項之Ljung-Box Q 殘差項序列相
關檢定--------------------------------------------83
表4-8 期貨與現貨之共整合檢定結果-----------------------85
表4-9 平均方程式殘差檢定-------------------------------87
表4-10 平均方程式之殘差項平方檢定----------------------88
表4-11 不對稱性診斷檢定--------------------------------89
表4-12 傳統迴歸模型估計結果----------------------------90
表4-13 VECM誤差修正模型估計結果------------------------92
表4-14 ECM-GARCH模型之估計結果-------------------------95
表4-15 VECM-GARCH(1,1)模型之估計結果-------------------99
表4-16 VECM-T-GARCH(1,1)模型之估計結果-----------------104
表4-17 樣本內不同模型避險效果之比較--------------------105
表4-18 樣本外不同模型避險效果之比較--------------------107
















圖 次
圖1-1 研究流程圖----------------------------------------6
圖4-1 公債期貨原始數列趨勢-----------------------------74
圖4-2 公債現貨原始數列趨勢-----------------------------74
圖4-3 公債期貨取對數趨勢-------------------------------75
圖4-4 公債現貨取對數趨勢-------------------------------75
圖4-5 公債期貨報酬數列趨勢-----------------------------76
圖4-6 公債現貨報酬數列趨勢-----------------------------76

參考文獻
中文部分
1.陳元保（1999）著，股市波動與經濟波動的因果關係，中華經濟研究院期刊，頁1-31。
2.陳增福（2002）著，應用LPMS法探求最適避險比率-以指數期貨與指數選擇權為例，國立高雄一科技大學財務管理所碩士論文。
3.林威助（2003）著，多變量GARCH架構下股價指數期貨避險策略之研究，國立台北大學企業管理學系碩士論文。
4.林婧文（2001）著，最適公債期貨避險策略之實證研究，國立高雄第一科技大學財務管理系碩士論文。
5.李儀坤， 張捷昌， 黃建森（2000）合著，金融風險管理，華泰文化。
6.吳宏達（2000）著，台股指數期貨與現貨之關聯性與預測-自我迴歸條件異質變異數族群模型之應用，國立台北大學統計學系碩士論文。
7.孫光政（2003）著，台股指數期貨避險比率與效果之實證研究—VECM-E-GARCH與VECM-GJR-GARCH之應用，國立台北大學合作經濟學系碩士論文。
8.黃馨慧（2003）著，台灣、日本、新加坡、韓國與美國股市關聯性之研究—VEC-TGARCH模型之運用，佛光人文社會學院經濟學系碩士論文。
9.黃紹儀（1999）著，期貨契約避險比率研究及績效分析—以SIMEX及TAIMEX為例，國立中興大學企業管理學系碩士論文。
10.黃景明（2002）著，台灣股價指數期貨最適避險策略之研究，私立淡江大學財務金融學系碩士論文。
11.楊育軒、李昱翰（2003）著，台灣與亞太股市資訊傳遞效果之研究－三元EGARCH模型之應用，第三屆提昇競爭力與經營管理研討會。
12.蔡瓊霈（2001）著，利率波動對殖利率曲線形狀之探究--蝶式交易策略之應用，國立台北大學企業管理學系碩士論文。
13.蔡依菁（2003）著，短期利率期貨與現貨關聯性之研究—以三個月期美國國庫券與歐洲美元為例，南華大學財務管理研究所碩士論文
14.賴昌作（2000）著，股價指數之避險比率與避險效益，國立台灣科技大學資訊管理研究所碩士班碩士論文。
15.葉銀華、蔡麗茹（2000）著，不同波動期間之期望報酬與風險關係的實證研究：不對稱GARCH-M模型之應用，輔仁管理評論，第七卷第二期。
16.魏志良（2001）著，國際股價指數期貨與現貨直接避險策略之研究，私立淡江大學財務金融學系碩士論文。
17.蘇啟仁（2003）著，美國股市及其總體經濟變數間關聯性與波動性之研究，國立台北大學合作經濟學系碩士論文。

英文部分
1.Bollerslev. T. (1986), “Generalised Autoregressive Conditional Heteroscedasticity” ,Journal of Econometrics, 33, pp.307-327.
2.Baillie, R.T. and R.J.Myers, (1991), “Bivariate GARCH Estimation of the Optimal Commodity Futures Hedge”, Journal of Applied Econometrics, Vol.6, pp.109-124.
3.Benet, B.A. (1992), “Hedge Period Length and Ex-Ante Futures Hedging Effectiveness： The Case of Foreign-Exchange Risk Cross Hedges”, Journal of Futures Markets, Vol.12, pp.163-175.
4.Cecchetti, S.G., R.E.Cumby, and S. Figlewski, (1988), “Estimation of Optimal Futures Hedge”, Review of Economics and Statistics, Vol.70, pp.623-630.
5.Chen, S. S., C. F. Lee., and K. Shrestha(2001), ”On a mean-generalized semivariance approach to determining the hedge ratio”, Journal of Futures Markets,Vol. 21, no.6, pp. 581-598.
6.Chan, K., K.C. Chan, and A.Karolyi, (1991), “Intraday Volatility in the Stock Index and Stock Index Futures Markets”, Review of Financial Studies, Vol.4, No.4, pp.657-684.
7.Chen Sheng-Syan,Cheng-few Lee,Keshab Shrestha (2003), ”Futures hedge ratios：a review”, The Quarterly Review of Journal of Economics and Finance, Vol.42, pp.433-465.
8.Dickey, D.A. and W. A. Fuller, (1979), “Distribution of the Estimates for Autoregressive Time Series with Unit Root”, Journal of the American statistical Association, Vol.74, No.366, pp.427-431.
9.Dickey, D. A. (1981), “Likelihood ratio statistics for autoregressive time series with a unit root”, Econometrica , Vol. 49, pp.1057-1072.
10.Ederington, L. H. (1979), ”The hedging performance of the new futures markets”, Journal of Finance, Vol. 34, no.1, pp.157-170.
11.Engle, R.F. and C.W.J.Granger, (1987),“Co-integration and Error Correction： Representation Estimation and Testing”, Econometrica, Vol. 55, No.2, pp.251-276.
12.Engle, R.F. (1982), “Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation”,Econometrics, Vol.50, pp.987-1007.
13.Eftekhari, B. (1998), ”Lower partial moment hedge ratios”, Applied Financial Economics, Vol. 8, pp. 645-652.
14.Engle, R. F., and K. Kroner (1995), “Multivariate simultaneous GARCH”, Econometric Theory, Vol. 11, pp.122-150.
15.Granger, C. W. J. and P. Newbold (1974), ”Spurious regression in econometrics”, Journal of Econometrics, Vol. 2, pp.111-120.
16.Howard, C.T. and L.J. D’Antonio, (1984), “A risk-return measure of hedging effectiveness”, Journal of Financial and Quantitative Analysis, Vol.19, No. 1, pp.373-381.
17.Kahl, K.H. (1983), “Determination of the Recommended Hedging Ratio”, American Journal of Agricultural Economics , Vol.65, pp.603-605.
18.Koutmos, G. (1998), “Asymmetries in the Conditional Mean and the Conditional Variance: Evidence From Nine Stock Markets,” Journal of Econometrics and Business, Vol. 50, pp. 277-290.
19.Lobo B. (2000), “Asymmetric Effects of Interest Rate Change On Stock Prices,” The Financial Review , Vol, 35, pp.125-44.
20.Lien, D., and Tse, Y.K. (2000), “Hedgeing downside risk with future contracts”, Applied financial Economics, Vol.10, pp.163-170.
21.Myers, R.J. (1991), “Estimating Time Varying Optimal Hedge Ratios on Futures Markets”, Journal of Futures Markets, Vol.11 No.1, pp.39-53.
22.Nelson, D.B. (1991), “Conditional Heteroskedasticity in Asset Returns：a New Approach,” Econometrica, Vol. 59, pp. 347-370.
23.Rabemananjara, R. and J.M. Zakoian (1993), “ThresholdARCH Models and Asymmetries in Volatility,” Journalof Applied Econometric, Vol.88, pp.31-49.
24.Said, S. and D.Dickey, (1984), “Testing for Unit Roots in Autoregressive-Moving Average Models with Unknown Order”, Biometrica, Vol.71, pp.599-607
25.Taufiq Choudhry (2003), ”Short-run deviations ans optimal hedge ratio：evidence from stock futures”, Journal of Multinational Financial Management, Vol.13, pp.171-192.
26.Witt, H.J., T.C.Schroeder, and M.L. Hayenga, (1987), “Comparison of Analytical Approaches for Estimating Hedge Ratios for Agricultural Commodities”, Journal of Futures Markets, Vol.7, No.2, pp.135-146.
27.Zakoian, J.M. (1990), “Threshold HeteroskedasticModels,” Manuscript, CREST, INSEE, Paris.
28.Zakoian, J. M. (1994)　“Threshold heteroskedasticmodel,” Journal of Economic Dynamics and Control 18, 931-955.