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系統識別號 U0002-1606200912380500
中文論文名稱 緩長記憶真實波動性與決定性波動函數在台指選擇權市場的預測能力分析
英文論文名稱 Forecasting Ability for Long Memory and Deterministic Volitility Function on TXO.
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 97
學期 2
出版年 98
研究生中文姓名 龔志澐
研究生英文姓名 Chih-Yun Kung
學號 696530772
學位類別 碩士
語文別 中文
口試日期 2009-05-19
論文頁數 134頁
口試委員 指導教授-段昌文
委員-陳達新
委員-林月能
委員-黃河泉
中文關鍵字 包含式迴歸  緩長記憶  ARFIMA  真實波動性 
英文關鍵字 encompassing regression  long memory  ARFIMA  realized volatility 
學科別分類 學科別社會科學商學
中文摘要 本文驗證台指選擇權在2001年12月到2008年5月間的選擇權價平 (at the money, ATM) 波動率、決定性波動函數 (deterministic volatility function, DVF) 的波動率與 ARFIMA 真實波動率 (realized volatility, RV),進一步分析包含式迴歸模型對台指選擇權隱含波動率之預測能力,特別地,本文以預測值作為其相依變數。
實證結果顯示,台股現貨指數之波動性不但有緩長記憶 (long memory),且適用以ARFIMA模型來配適。互相比較三個預測變數之下,預測模型以DVF對全契約的隱含波動率預測能力最佳,此外,同時加入三個波動性預測值之後的包含式迴歸,其對全契約的隱含波動率預測能力最高,樣本外的預測誤差亦為最小。
最後,為了驗證包含式迴歸模型的預測能力,本文須檢視其在台指選擇權市場能否獲利。透過風險中立 (delta neutral) 的選股策略,本文建構跨式 (straddle) 投資組合的交易策略。投資績效顯示,以同時加入ARFIMA真實波動率和決定性波動函數預測值之兩變數包含式迴歸,其一週投資績效為最佳;此外,上述預測誤差最小之包含式迴歸模型,不論在有無考慮交易成本下,皆可獲得正向報酬。
英文摘要 The paper estimates the implied volatilities of the at-the-money (ATM) option, deterministic volatility function (DVF) and realized volatility (RV) using ARFIMA model derived from TAIFEX options on Taiwan stock index during December 2001 to May 2008. We compare the predictive ability of encompassing regression model, especially, we use the predicted values as independent variables.
The results indicate that we confirm not only the presence of long memory behavior in the TX volatility but also accurately fitted by ARFIMA. Comparing the different predictive variables, we find the DVF model has the highest forecasting ability of implied volatility for call and put options. Moreover, after including three predictive variables, the encompassing regression has the highest forecasting ability of the implied volatility in the sample and the smallest forecasting error out of the sample for call and put options.
Finally, in order to examine the forecasting ability of the encompassing regression model, we need to tell whether implied volatility forecasts can be used to formulate profitable out-of-sample trading strategies in TXO market or not. By using delta-neutral option, we construct straddle portfolios to estimate benefits of trading strategies. The results show that the encompassing regression with the realized volatility and DVF volatility of one week straddle portfolio has the best performance. Furthermore, regardless of the transaction cost, the encompassing regression with the smallest forecasting error can get positive return in TXO market.
論文目次 中文摘要 I
英文摘要 II
目 次 III
表 次 IV
圖 次 VI
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、研究架構 5
第二章、文獻探討 6
第一節、真實波動率 6
第二節、隱含波動率 10
第三節、波動率的緩長記憶 18
第四節、波動率的預測 25
第五節、預測誤差的衡量 31
第六節、交易策略 33
第三章、研究設計與方法 35
第一節、取樣標準與研究設計 35
第二節、波動率的估計 46
第三節 包含式迴歸分析 56
第四節、預測能力的衡量指標 58
第五節、投資策略的設計 60
第四章、實證結果 62
第一節、波動率 62
第二節 包含式迴歸 79
第三節、樣本內與外的預測 103
第四節 投資績效的評估 109
第五章 結論 114
參考文獻 116
附錄表 123

表次
【表1】使用單一模型預測波動率的文獻整理 27
【表2】買賣權價內與價外程度分類表 38
【表3】包含式迴歸變數 45
【表4】買權隱含波動率依價性分類之敘述統計量 64
【表5】賣權隱含波動率依價性分類之敘述統計量 65
【表6】選擇權契約之隱含波動率估計值敘述統計表 67
【表7】價平選擇權之隱含波動率預測值敘述統計表 69
【表8】決定性波動函數之波動率預測值敘述統計表 71
【表9】ARFIMA(1, d, 0)真實波動率預測值之敘述統計表 77
【表10】單一ARFIMA真實波動率對TXO之隱含波動率預測能力迴歸表 81
【表11】單一ARFIMA真實波動率對TXO買權之隱含波動率預測能力迴歸表 82
【表12】單一ARFIMA真實波動率對TXO賣權之隱含波動率預測能力迴歸表 83
【表13】單一價平選擇權對TXO之隱含波動率預測能力迴歸表 84
【表14】單一決定性波動函數對TXO之隱含波動率預測能力迴歸表 84
【表15】對TXO買權隱含波動率之包含式迴歸 89
【表16】對TXO賣權隱含波動率之包含式迴歸 90
【表17】對TXO不分買賣權契約隱含波動率之包含式迴歸 91
【表18】ARFIMA真實波動率加入Jump對TXO買權契約隱含波動率之包含式迴歸 92
【表19】ARFIMA真實波動率加入Jump對TXO賣權契約隱含波動率之包含式迴歸 93
【表20】ARFIMA真實波動率加入Jump對TXO不分買賣權契約隱含波動率之包含式迴歸 94
【表21】ARFIMA真實波動率加入Leverage effect對TXO買權契約隱含波動率之包含式迴歸 95
【表22】ARFIMA真實波動率加入Leverage effect對TXO之賣權契約隱含波動率包含式迴歸 96
【表23】ARFIMA真實波動率加入Leverage effect對TXO之不分買賣權契約隱含波動率包含式迴歸 97
【表24】ARFIMA真實波動率同時加入Jump和Leverage effect對TXO之買權契約隱含波動率包含式迴歸 98
【表25】ARFIMA真實波動率同時加入Jump和Leverage effect對TXO之賣權契約隱含波動率包含式迴歸 99
【表26】ARFIMA真實波動率同時加入Jump和Leverage effect對TXO不分買賣權契約隱含波動率之包含式迴歸 100
【表27】買權情況下的預測誤差表 107
【表28】不分買賣權情況下的預測誤差表 108
【表30】近月份包含式迴歸預測的波動率用於模擬投資之績效 111
【附錄表2】對TXO賣權隱含波動率之包含式迴歸 124
【附錄表3】對TXO不分買賣權隱含波動率之包含式迴歸 125
【附錄表4】ARFIMA真實波動率加入Jump對TXO買權隱含波動率之包含式迴歸 126
【附錄表5】ARFIMA真實波動率加入Jump對TXO賣權隱含波動率之包含式迴歸 127
【附錄表6】ARFIMA真實波動率加入Jump對TXO不分買賣權隱含波動率之包含式迴歸 128
【附錄表7】ARFIMA真實波動率加入Leverage effect對TXO買權隱含波動率之包含式迴歸 129
【附錄表8】ARFIMA真實波動率加入Leverage effect對TXO賣權隱含波動率之包含式迴歸 130
【附錄表9】ARFIMA真實波動率加入Leverage effect對TXO不分買賣權隱含波動率之包含式迴歸 131
【附錄表10】ARFIMA真實波動同時加入Jump和Leverage effect對TXO買權隱含波動率之包含式迴歸 132
【附錄表11】ARFIMA真實波動率同時加入Jump和Leverage effect對TXO賣權隱含波動率之包含式迴歸 133
【附錄表12】ARFIMA波動率同時加入Jump和Leverage effect對TXO不分買賣權隱含波動率之包含式迴歸 134

圖次
圖1、決定性波動函數之隱含波動率預測值估計示意圖 42
圖2、台股指數與隱含波動率圖 62
圖3、樣本內全期間隱含波動率次數直方圖 68
圖4、近月份隱含波動率次數直方圖 69
圖5、樣本內全期間ATM隱含波動率次數直方圖 70
圖6、近月份ATM隱含波動率次數直方圖 70
圖7、樣本內全期間DVF波動率次數直方圖 72
圖8、近月份DVF波動率次數直方圖 72
圖9、不同樣本頻率下的年平均真實波動率 73
圖10、真實波動率在不同樣本頻率下之ACF圖 74
圖11、ARFIMA(1, d, 0)模型之各單位期間d值圖 75
圖12、RV、IV和ATM波動率預測值之對照圖 76

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