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系統識別號 U0002-2605200619012100
中文論文名稱 GARCH系列模型與台指選擇權VIX指數波動性預測能力之比較
英文論文名稱 A Comparison of the Forecasting Performance between GARCH family Models and VIX on TAIEX Options
校院名稱 淡江大學
系所名稱(中) 財務金融學系碩士班
系所名稱(英) Department of Banking and Finance
學年度 94
學期 2
出版年 95
研究生中文姓名 曾彥錤
研究生英文姓名 Yen-Chi Tseng
學號 693490491
學位類別 碩士
語文別 中文
口試日期 2006-05-19
論文頁數 69頁
口試委員 指導教授-謝文良
共同指導教授-李進生
委員-林允永
委員-鍾惠民
委員-陳達新
中文關鍵字 波動性  一般化自我迴歸條件異質變異數模型  波動性指數 
英文關鍵字 Volatility  GARCH Model  GJR-GARCH Model  VIX 
學科別分類 學科別社會科學商學
中文摘要 由於金融資產的波動性在金融市場(尤其是在台灣這個具有高波動性的市場)扮演重要角色,無論是在風險管理或是衍生性商品的訂價、選擇權的交易與避險等等方面,如何準確預測波動性,一直都是相當重要的課題。本文使用一般化自我迴歸條件異質變異數模型(GARCH)及其修正模型(GJR-GARCH)與台灣期交所所編制台指選擇權波動性(VIX)指數之預測能力來比較,希望找出適合描述台灣金融市場波動性模型。
實證發現,以日資料進行預測績效時,GJR-GARCH模型表現較為優秀;若以日內資料來估計時,各個模型的解釋能力皆明顯提高許多且誤差也相對改善。因此,我們可以肯定頻率越密集的資料可獲得更高的解釋能力、更低的預測誤差、與更多的資訊內涵。綜合本文研究,日內報酬台指選擇權波動性指數(VIX)在平均絕對誤差(MAE)與均方根誤差(RMSE)的評估上,雖然並非最好,但似乎是預測真實波動性的不偏估計值。
英文摘要 Volatility forecasting is very important to derivative pricing, hedging, and risk management. This paper using GARCH, GJR-GARCH models and the VIX index of TAIEX Options to compare their forecasting ability.
The empirical evidence show that using daily data to forecast the performance, GJR-GARCH model is superior, while using intraday data, the explanatory power of all models are obviously enhanced and errors are also improved. Therefore, we approve that the more intensive data can obtain the higher explanatory power, lower forecasting errors and more information content.
In summary, we find that the VIX index of TAIEX Options using intraday data seems an unbiased estimator to forecast the real volatility, although it does not have the best performance than other models in MAE and RMSE testing indicators.
論文目次 目錄
中文摘要............................................................I
英文摘要............................................................II
目錄..................................................................III
表目錄...............................................................IV
圖目錄...............................................................V

第一章 序論.....................................................1
第一節 研究背景與動機.....................................1
第二節 研究目的...............................................5
第三節 研究架構...............................................6
第四節 研究流程...............................................6

第二章 文獻回顧...............................................8
第一節 波動性簡介............................................8
第二節 傳統時間序列模型..................................10
第三節 隱含波動性............................................12
第四節 波動性模型預測能力之比較.....................16

第三章 研究方法...............................................26
第一節 真實波動性的衡量..................................26
第二節 時間數列的波動性模型............................28
第三節 隱含波動VIX模型....................................32
第四節 模型預測能力之比較...............................38

第四章 實證結果分析..................................................40
第一節 樣本的敘述統計特性........................................40
第二節 資料處理與敘述..............................................44
第三節 波動性模型之檢定與參數估計...........................47
第四節 波動性模型之預測能力比較分析........................52
第五節 時間序列模型與VIX指數模型之預測誤差比較......55

第五章 結論與建議.........................................58
第一節 結論...................................................58
第二節 研究限制............................................59
第三節 建議...................................................60

參考文獻......................................................61
中文部份......................................................61
英文部份......................................................62

附錄 A........................................................66
附錄 B........................................................69

表目錄

【表4-1】:台灣加權指數每日、日內及VIX每日、日內交易資料
之敘述統計結果.........................................................................43
【表4-2】:ADF恆定性檢定.......................................................46
【表4-3】:LB-Q檢定................................................................46
【表4-4】:變異數齊一性(LM)檢定.............................................48
【表4-5】:每日報酬GARCH參數估計........................................50
【表4-6】:每日報酬GJR參數估計..............................................51
【表4-7】:日內報酬GARCH參數估計.........................................51
【表4-8】:日內報酬GJR參數估計..............................................52
【表4-9】:波動性模型預測能力之比較.......................................55
【表4-10】:預測誤差比較.........................................................56

圖目錄

【圖一】台灣加權指數選擇權歷年日均量比較..................................................2
【圖二】研究架構流程圖...............................................................................7
【圖三】台灣加權指數每日報酬(2005年1月至10月)........................................41
【圖四】台灣加權指數日內(每五分鐘)報酬(2005年1月至10月).........................42
【圖五】每日報酬各模型波動性比較.............................................................57
【圖六】日內報酬各模型波動性比較.............................................................57
參考文獻 參考文獻
一、中文部份
1.鄭義、胡僑芸、林忠義,(2005),波動率指數VIX於臺指選擇權市場之應用,TAIFEX REVIEW,Vol.7,13-33。

2.莊益源、張鐘霖、王祝三,(2003),波動率模型預測能力的比較-以台指選擇權為例,台灣金融季刊,第4輯第2期,41-63。

3.林楚雄、劉維琪、吳欽衫,(1999),台灣股票店頭市場股價報酬波動行為的研究,企業管理學報,第44期,165-192。

4.林楚雄、劉維琪、吳欽衫,(1999),不對稱GARCH模型的研究,企業管理學報,第16卷第3期,479-515。

5.王甡,(1995),報酬衝擊對條件波動所造成之不對稱效果-台灣股票市場之實證分析,證券市場發展季刊,第7卷第1期,125-160。

6.胡僑芸,(2003),台指選擇權VIX指數之編製,中山大學財務管理研究所碩士論文。

7.李進生、鍾惠民、陳煒朋,(2000),不同波動性模型預測能力之比較:台灣與香港認購售權證市場實證,證券市場發展季刊,第11卷第4期,57-90。

8.陳煒朋,(1999),GARCH 模型與隱含波動性模型預測能力之比較,淡江大學財務金融所碩士論文。

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二、英文部分
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19.Fleming, J., (1998). The Quality of Market Volatility Forecasts Implied by S&P100 Index Options Prices, Journal of Empirical Finance, 5,317-345.

20.Gokcan, S., (2000). Forecasting Volatility of Emerging Stock Markets: Linear versus Non-linear GARCH Models, Journal of Forecasting, 19, 499-504.

21.Glosten, L., R. Jagannathan and D. Runkle, (1993). On the Relation Between the Expected Value and the Volatility on the Nominal Excess Returns on Stock, Journal of Finance, 48, 1779-1801.

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26.Lamoureux, C. and W. Lastrapes, (1993). Forecasting Stock-return Variances: Toward an understanding of stochastic implied volatilities, Review of Financial Studied, 6, 293-326.

27.Lopez, J., (2001). Evaluating the predictive accuracy of volatility models, Journal of Forecasting, 20, 87–109.

28.McMillan, D.G. and E.H. Speight, (2004). Daily Volatility Forecasts: Reassessing the Performance of GARCH Models, Journal of Forecasting, 23, 449–460.

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30.Park, B.J., (2002). An Outlier Robust GARCH Model and Forecasting Volatility of Exchange Rate Returns, Journal of Forecasting, 21, 381–393.

31.Richard, T.B and P.D. Ramon, (1990). Stock Returns and Volatility, Journal of Financial and Quantitative Analysis, 25, 203-214.

32.Udo, S.M., (1997). Volatility Forecasting with Nonlinear and Linear Time Series Models: A Comparison.
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