在本文中，我們透過KOSPI每分鐘的高頻資料，將交易日劃分為不同日內時段來估算買賣價差。我們比較了三種不同計算價差的方法，包括計算結果為日頻的Roll (1984) 估計法，與計算結果可以高於日頻的 Cowin and Schultz (2012) 估計法 (CS) 與 Li, Lambe and Adegbite (2018) 的 Basic High and Low (BHL) 估計法。我們的實證結果顯示Roll價差每天的平均值和標準差隨著樣本頻率的增加而減小。而高低價差模型的標準差同樣隨樣本區間縮小而減少，並估計價差在半天區間時較每日與十分鐘區間有較少為負的結果。另外，與BHL估計模型相較下，CS模型估計的平均值和標準差更小。對於使用高低價估計的價差模型，我們發現存在日內型態，並且所得出的價差會隨交易時間經過變小。其中日內型態也同樣呈現於負價差，透過價差為負值佔全部價差的比例來看，CS模型的估計值在開盤時較BHL模型容易為負值，並在接近中午時顯示相反的結果。我們推斷較高百分比的CS價差可能是由較高的價格波動導致的。另外，我們確認了隔夜報酬對日價差的影響，當隔夜報酬較大且為負時，效果更強。

In this paper, we examine the performance of three bid-ask spread estimators using high-frequency KOSPI data by dividing each trading day into several intraday periods. The three methods are Roll (1984), Cowin and Schultz (2012), hereafter CS, and the Basic High and Low (BHL) estimator of Li, Lambe and Adegbite (2018). With high-frequency data, the Roll estimator gives daily spread values, while the CS and BHL methods give spread estimates for intraday intervals. Our empirical results show that the mean value and standard deviation of daily Roll spreads decrease with higher sampling frequencies. High-low spreads also have decreasing standard declines when interval is smaller and lower percentage of negative spreads at half-day interval than one-day and 10-minute intervals. Compared with BHL estimator, CS estimator has smaller mean and standard deviation. There exists an intraday pattern in CS and BHL spreads, with average spread values decreasing as trading hours proceed. We also study the distribution of negative spread values and find that CS spreads are more likely to be negative than BHL spreads at market open, but this relationship reverses near the middle of day. We infer that the higher percentage of negative CS spreads may be due to higher price volatility. In addition, we identify overnight returns as a plausible factor for estimated spreads being negative, and this effect is stronger when overnight returns are negative.

論文審定書 i
摘要 ii
Abstract iii
Table of Contents iv
List of Figures v
List of Tables vi
1 Introduction 1
2 Literature review 5
3 Data 8
4 Method and Model 17
4.1 The Roll estimator 17
4.2 The CS estimator 18
4.3 The BHL estimator 20
5 Estimation and results 22
5.1 Summary statistics 22
5.2 Intraday pattern of CS and BHL estimators 23
5.3 Overnight Return and CS, BHL estimators 26
6 Conclusions 35
References 36

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