臺灣博碩士論文加值系統

本文主要是以馬可夫轉換模型（Markov Regime Switching Model；MRS）來探討台灣股價指數期貨之最適避險比率。在過去的文獻裡，期貨與現貨之最適避險比率多是以雙變量GARCH模型來作探討，因為雙變量GARCH模型能探討期貨與現貨報酬的波動現象與交互影響效果，但根據Alizadeh and Nomikos（2004）說明，期貨與現貨報酬的動態相互關係可能具有狀態轉換的特性，因此建議，期貨與現貨之避險比率可能取決於市場狀態的影響，此外Sarno and Valente（2000）也以狀態轉換模型解釋期貨與現貨價格之間的相互關係，其效果比簡單線性迴歸模型佳，所以本文即以馬可夫轉換模型來探討台灣股價指數期貨之最適避險比率。除此之外，本研究也加入隨機係數自迴歸模型（Random Coefficient Autoregressive model；RCAR）來探討期貨與現貨報酬間的動態關係。所以本研究在避險比率的探討上，除了以上兩個模型外，也加入其它模型（如：雙變量GARCH、OLS、Naïve…等模型）來加以比較並探討不同避險模型之避險績效。
最後從本文的實證結果得知，隨機係數自迴歸模型在樣本內（in-sample）的估計上優於其它避險模型，而馬可夫轉換模型次之；但樣本外（out-of-sample）的預測能力，雙變量GARCH模型則比其它避險模型好，隨機係數自迴歸模型次之。所以本研究建議，當投資者在操作避險策略時，不同商品間可能存在的各種相互關係均是投資者或風險管理者所要仔細考量的。

This research primarily uses Markov Regime Switching model to investigate the optimal hedge ratio between Taiwan Stock Index and Taiwan Future Exchange (TAIFEX). In the past researches, when it comes to hedge ratio between spot and future markets, Bivariate-GARCH model is often used. This is because that Bivariate-GARCH model is able to catch the interaction between these two markets.On the other hand, Alizadeh and Nomikos（2004）claimed that there may be different regimes in the interaction between stock index and index future. Therefore, hedge ratios may depend on different regimes. Also, Sarno and Valente（2000）found Regime Switching Model outperforms OLS when investigating the relationship between stock index and index futures price. Thus, this research examines the optimal hedge ration in TAIFEX with Markov Regime Switching model.This research also takes Random Coefficient Autoregressive model (RCAR) and other models into consideration, such as Bivariate GARCH model, OLS, and Naïve, to compare the hedge efficiency between all models.
Finally, the empirical result shows: RCAR outperforms other models in-sample, and MRS model is next to it; asymmetric Bivariate GARCH has better out-of-sample performance than other models, and RCAR Model is only second to it. Therefore, this research suggests that investors will be able to enhance efficiency in hedge strategy if they could take account of different regimes.

摘要 i
誌謝 iii
目次 iv
表目錄 vii
圖目錄 viii
第一章 緒論 1
1.1 研究背景與動機 1
1.2 研究目的 3
1.3 本文架構 4
1.4 研究流程圖 5
第二章 文獻回顧 6
2.1 股價指數期貨之功能與避險理論 6
2.1.1 股價指數期貨之功能 6
2.1.2 避險理論 7
2.2 最適避險比率之文獻探討 10
2.2.1 固定避險比率 11
2.2.2 動態避險比率 12
第三章 研究方法 17
3.1 單根檢定 17
3.1.1 定態與非定態 17
3.1.2 Dickey-Fuller單根檢定 18
3.1.3 ADF單根檢定 19
3.2 共整合的檢定 20
3.2.1 共整合的概念 20
3.2.2 共整合的檢定 21
3.3 最適避險比率的推導 24
3.4 避險模型 27
3.4.1 天真避險 27
3.4.2 靜態避險 27
3.4.3 馬可夫轉換模型與最適避險比率 28
3.4.4 隨機係數自迴歸模型 42
3.4.5 Bivariate GARCH Model與動態避險比率 48
3.4.6 Bivariate GARCH-CI模型 51
3.5 績效衡量 52
第四章 實證研究 53
4.1 資料來源與分析 53
4.2 單根檢定 54
4.3 共整合檢定 55
4.4 MRS模型與RCAR模型的估計結果 56
4.5 Bivariate GARCH模型的估計結果 59
4.6 圖形分析 61
4.7 避險績效的探討 64
第五章 結論與建議 66
5.1 結論 66
5.2 建議 67
參考文獻 68
附錄
A 馬可夫模型估計流程圖 73
B Kalman Filter模型估計流程圖 74

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