本文以2001年12月至2008年5月間之台灣加權指數 (TX)、台指選擇權 (TXO)與台指期貨(TXF)日內及日資料，進一步於包含式模型中分別加入歷史波動率 (history volatility, HV)、真實波動率 (realized volatility, RV)、價平選擇權隱含波動率 (at-the money option impilied volatility, ATM)、決定性波動率函數 (deterministic volatility function, DVF) 等波動率預測模型之預測能力，並驗證TXF或台指指數何者可做為投資TXO市場之參考標的物。
    實證結果顯示，由波動率預測模型之調整後R2以及相關係數分析指出，TXF之波動率預測模型對於TXO隱含波動率有較佳的解釋能力，其中以TXF之移動平均天數為十天的歷史波動率以及取樣頻率為9分鐘之真實波動率的解釋能力較高；由此證據顯示，相對於台指指數，TXF可為對於投資TXO市場較佳的參考標的物。投資績效顯示，無論是買賣買權或賣權的投資策略皆可獲得正向報酬；若在考慮交易成本下，則是以持有期間為五天之投資績效多能獲得正向的報酬。

This paper puts the volatility-forecasting models, including history volatility(HV), realized volatility(RV), at-the money option implied volatility(ATM) and deterministic volatility function(DVF) into the encompassing regression to examine the forecasting ability of volatility model for TX, TXO and TXF during December 2001 to May 2008. Also, we verify that TXF or TX which is the better reference object for investing in TXO market. Based on the results of the adjusted-R2 and correlation coefficient of volatility-forecasting models, we find that the forecasting ability for the implied-volatility of TXO is better with volatility-forecasting models of TXF than TX.
     For the forecasting-models of TXF, the history volatility which is estimated by 10-day moving average and the realized volatility which is estimated by 9-minute intraday sampling frequency have the higher explanation ability. By above-mentioned, we can prove that TXF is the better reference object for investing in TXO market than TX. However, in the analysis of investment strategy, the results indicate that the strategy has positive performance, regardless of call or put option strategy. Our results also show that only the investment strategy of 5-day holding period has the positive performance with the consideration of transaction cost.

目 錄
目 錄	V
表目錄	VI
圖目錄	VIII
附錄	IX
第一章、緒論	1
第一節、研究動機	1
第二節、研究目的	3
第三節、論文架構	3
第二章、文獻探討	6
第一節、歷史波動率與真實波動率	6
第二節、隱含波動率模型	13
第三節、波動率的預測	20
第四節、包含式迴歸	23
第五節、投資績效的衡量	24
第六節、現貨與衍生性商品市場之領先-落後關係與價格發現之相關文獻	25
第三章、波動率模型	28
第一節、歷史波動率	28
第二節、真實波動率	29
第三節、隱含波動率與決定性波動率函數模型	30
第四章、研究設計與方法	33
第一節、取樣標準與研究設計	33
第二節、歷史波動率、真實波動率的估計	38
第三節、隱含波動率的估計	42
第四節、包含式迴歸分析	44
第五節、波動率模型預測能力檢定	45
第五節、投資績效的設計	47
第五章、實證結果	48
第一節期貨與現貨波動率估計結果	48
第二節 包含式迴歸分析結果	62
第三節、樣本內與外的預測結果	102
第四節、投資績效的衡量	109
第六章、結論	118
參考文獻	122
附錄	129
表目錄
表5-1-1 TXO隱含波動率之敘述統計量	49
表5-1-2買權隱含波動性依價性分類之敘述統計量	50
表5-1-3賣權隱含波動性依價性分類之敘述統計量	50
表5-1-4台指指數、TXF真實波動率估計值統計量表	55
表5-1-5台指指數、TXF之歷史波動模型預測值統計量	58
表5-1-6台指指數、TXF真實波動率預測值統計量	59
表5-1-7 ATM隱含波動率及其預測值之統計量	60
表5-1-8決定性波動率函數模型之預測值統計量	61
表5-2-1對台指指數9分鐘真實波動率之單一變數包含式迴歸結果	64
表5-2-2對台指指數15分鐘真實波動率之單一變數包含式迴歸結果	65
表5-2-3對台指指數30分鐘真實波動率之單一變數包含式迴歸結果	66
表5-2-4對台指指數9分鐘真實波動率之雙變數包含式迴歸結果	68
表5-2-5對台指指數15分鐘真實波動率之雙變數包含式迴歸結果	69
表5-2-6對台指指數30分鐘真實波動率之雙變數包含式迴歸結果	70
表5-2-7對台指指數9分鐘真實波動率之多變數包含式迴歸結果	72
表5-2-8對台指指數15分鐘真實波動率之多變數包含式迴歸結果	73
表5-2-9對台指指數30分鐘真實波動率之多變數包含式迴歸結果	74
表5-2-10對TXF 9分鐘真實波動率之單變數包含式迴歸結果	76
表5-2-11對TXF 15分鐘真實波動率之單變數包含式迴歸結果	77
表5-2-12對TXF 30分鐘真實波動率之單變數包含式迴歸結果	78
表5-2-13對TXF 9分鐘真實波動率之雙變數包含式迴歸結果	80
表5-2-14對TXF 15分鐘真實波動率之雙變數包含式迴歸結果	81
表5-2-15對TXF 30分鐘真實波動率之雙變數包含式迴歸結果	82
表5-2-16對TXF 9分鐘真實波動率之多變數包含式迴歸結果	84
表5-2-17對TXF 15分鐘真實波動率之多變數包含式迴歸結果	85
表5-2-18對TXF 30分鐘真實波動率之多變數包含式迴歸結果	86
表5-2-19對不分買賣權的TXO隱含波動率之單變數包含式迴歸結果	88
表5-2-20對買權的TXO隱含波動率之單變數包含式迴歸結果	89
表5-2-21對賣權的TXO隱含波動率之單變數包含式迴歸結果	90
表5-2-22對不分買賣權的TXO隱含波動率之雙變數迴歸結果表	92
表5-2-23對買權的TXO隱含波動率之雙變數迴歸結果表	93
表5-2-24對賣權的TXO隱含波動率之雙變數迴歸結果表	94
表5-2-25對不分買賣權的TXO隱含波動率之多變數包含式迴歸結果	98
表5-2-26對買權的TXO隱含波動率之多變數包含式迴歸結果	99
表5-2-27對賣權的TXO隱含波動率之多變數包含式迴歸結果	100
表5-2-28 TXO隱含波動率與自變數之相關係數表	101
表5-2-29對台指指數真實波動率之多變數包含式迴歸結果	101
表5-3-1台指指數各分鐘真實波動率預測模型之預測結果	105
表5-3-2 TXF各分鐘真實波動率預測模型之預測結果	106
表5-3-3 TXO隱含波動率預測模型之預測結果	107
續表5-3-3 TXO隱含波動率預測模型之預測結果	108
表5-4-1對台指指數真實波動率之預測模型持有一天之投資績效	112
表5-4-2對台指指數真實波動率之預測模型持有五天之投資績效	113
表5-4-3對 TXF真實波動率之預測模型持有一天之投資績效	114
表5-4-4 對TXF真實波動率之預測模型持有五天之投資績效	115
表5-4-5 對TXO隱含波動率之預測模型持有一天之投資績效	116
表5-4-6 對TXO隱含波動率之預測模型持有五天之投資績效	117
圖目錄
圖1-1研究流程圖	5
圖4-1 台指指數與TXF走勢圖	33
圖4-2 歷史波動率移動平均示意圖	39
圖5-1-1真實波動率在不同取樣頻率下之年平均值圖	52
圖5-1-2 台指指數與TXF之真實波動率在各個取樣頻率下的比較圖	53
圖5-1-3 台指指數9分鐘、15分鐘、30分鐘真實波動率與台指指數走勢圖	54
附錄
表1台指指數5天之歷史波動率EACF表	129
表2台指指數10天之歷史波動率EACF表	130
表3台指指數20天之歷史波動率EACF表	131
表4 TXF 5天之歷史波動率EACF表	132
表5 TXF 10天之歷史波動率EACF表	133
表6 TXF 20天之歷史波動率EACF表	134
表7台指指數歷史波動率預測模型檢定值	135
表8 TXF 歷史波動率預測模型檢定值	136
表9對台指指數真實波動率之預測模型持有一天之投資績效	137
表10對台指指數真實波動率之預測模型持有五天之投資績效	138
表11對 TXF真實波動率之預測模型持有一天之投資績效	139
表12 對TXF真實波動率之預測模型持有五天之投資績效	140
表13 對TXO隱含波動率之預測模型持有一天之投資績效	141
表14 對TXO隱含波動率之預測模型持有五天之投資績效	142
圖1台指指數歷史波動率估計值之ACF圖	143
圖2 TXF歷史波動率估計值之ACF圖	143

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