如何從交易價格資料推估價差為財務文獻之一重要研究主題。本文探討基於全距之價差估計模型，使用兩種方式計算價差，分別為Cowin and Schultz (2012)估計法 (CS) 與Li, Lambe, and Adegbite (2018) 的Basic High and Low (BHL) 估計法，使用四種不同市場(KOSPI200、NIKKEI225、FTSE100、ESTX50) 30分鐘的日內資料並與日資料結果進行對照。我們發現無論是日資料或30分鐘資料， 兩種價差計算方式皆容易產生價差為負的情形，而負價差之比例介於 30-50%。為改進此問題，我們使用了Chou (2005) 的條件自我回歸全距模型 (Conditional Autoregressive Range, CARR)，將原本價差使用CARR模型求得條件期待值後代入計算公式，我們發現此修正做法能有效減少負價差出現頻率。我們也進一步在CARR模型中考慮波動度之槓桿效果，亦即加入前期報酬為負之指標函數，以提升對價差計算結果的表現。

In this paper, four different markets (KOSPI200, NIKKEI225, FTSE100, ESTX50) were used with high-frequency data of 30-minute intervals to estimate the price spread and compared the result with daily data. Two methods were used to calculate the price spread: Corwin and Schultz's estimation method (CS) and Li, Lambe, and Adegbite (2018)’s Basic High and Low (BHL) estimation method. In addition to the original data's price spread, the Weibull CARR model published by Chou (2005) was also used to obtain an optimized range of the price spread, improving the spread estimation compared to the unprocessed version. We further considered yesterday's return,　so we added an indicator function into the WCARR model and try to improve its performance.

論文審定書.....................................................................................................................i
摘要................................................................................................................................ii
Abstract........................................................................................................................ iii
目錄...............................................................................................................................iv
圖次................................................................................................................................v
表次...............................................................................................................................vi
第一章、緒論................................................................................................................1
第二章、文獻回顧........................................................................................................3
第一節 基於全距之價差模型...............................................................................3
第二節 全距波動模型...........................................................................................4
第三節 波動度槓桿效果.......................................................................................5
第三章、資料來源........................................................................................................6
第一節資料前處理................................................................................................6
第二節 調整日內波動型態 (Intraday Volatility Pattern) .....................................7
第四章、研究方法........................................................................................................8
第一節 CS 模型....................................................................................................8
第二節 BHL 模型.................................................................................................9
第三節 自我回歸模型.........................................................................................10
第五章、實證結果......................................................................................................13
第一節 歷史資料計算結果.................................................................................13
第二節 使用 CARR 計算條件期待值後估計價差............................................13
第三節 考慮事後資料問題.................................................................................14
第四節 負價差分布情形.....................................................................................14
第五節 平均價差的日內分布.............................................................................15
第六章、結論..............................................................................................................16
References....................................................................................................................17

圖次
圖 3- 1 各市場 IVP 柱狀圖.........................................................................................24
圖 5- 1 韓國市場負價差數量加總圖………………………………………………..30
圖 5- 2 歐洲市場負價差數量加總圖 .........................................................................31
圖 5- 3 英國市場負價差數量加總圖 .........................................................................32
圖 5- 4 日本市場負價差數量加總圖 .........................................................................33
圖 5- 5 韓國市場平均價差圖 .....................................................................................34
圖 5- 6 歐洲市場平均價差圖 .....................................................................................35
圖 5- 7 英國市場平均價差圖 .....................................................................................36
圖 5- 8 日本市場平均價差圖 .....................................................................................37

表次
表 3- 1 各市場 30 分鐘資料敘述統計 .......................................................................20
表 3- 2 各市場日資料敘述統計 .................................................................................22
表 5- 1 各市場以原始全距估計之敘述統計………………………………………..25
表 5- 2 各市場以 WCARR 估計之敘述統計.............................................................26
表 5- 3 各市場以 WCARR+I 估計之敘述統計 .........................................................27
表 5- 4 各市場考慮事後資料問題後以日資料估計之敘述統計 .............................28
表 5- 5 各市場考慮事後資料問題後以 30 分鐘資料估計之敘述統計....................29

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