本研究藉由將單一交易日分割為許多區間，以收集更多高低價比值樣本，並用以計算價差估計值。研究結果顯示當區間長度超過30分鐘時，高低價差估計法的估計效率較Roll估計法為優。具體地說，當區間長度分割為50至70分鐘時，高低價差估計法的百分比誤差會降至最低。相對而言，當區間長度短於20分鐘時，Roll估計法的估計效率則優於高低價差估計法，並出現較低的百分比誤差。

By dividing a trading day into several intraday periods, a greater number of samples of high-low ratio are collected to compute a fractional high-low spread estimator. With a dataset of the length of intraday period longer than 30 minutes, fractional high-low spread estimators surpass Roll spread estimators. Specifically, to minimize percentage error of a fractional high-low spread estimator, the optimal length of intraday period should be chosen between 50 to 75 minutes. In contrast, with a dataset of the length of intraday period shorter than 20 minutes, Roll estimators outperform fractional high-low spread estimators in a lower percentage error.

目錄

第一章 前言及文獻探討 01
第二章 研究方法 03
第一節 研究模型 03
第二節 估計效率和測量誤差 05
第三章 模擬程序及模擬結果 07
第一節 模擬程序 07
第二節 模擬結果 09
第四章 強度分析 13
第一節 價差大小的影響 13
第二節 交易頻率的影響 13
第三節 波動的影響 15
第四節 價格聚集和價格反轉的影響 15
第五節 討論與建議 17
第五章 研究資料與實證結果 25
第六章 研究成果 27
附錄 28
參考文獻 29

表目錄

表一 價差為0.5％時的高低價差估計效率10
表二 S=1%與S=3%時的百分比誤差和MSE14
表三 交易頻率每分鐘12筆與30筆時的價差估計百分比誤差和MSE16
表四 每日波動幅度 σ=0.02與 σ=0.04時的價差估計百分比誤差與MSE19
表五 價差估計在價格聚集及價格反轉時的百分比誤差與MSE22
表六 表一至表五中，不同價差估計在每種情況下的相對精確度23
表七 表一至表五中，每種情況下的最佳盤中週期長度24
表八 台股指數期貨0天內到期合約的價差估計26

圖目錄

圖1-1 未調整的高低價差估計在不同程度序列相關下的百分比誤差20
圖1-2 調整後的高低價差估計在不同程度序列相關下的百分比誤差21

apGwilym, O. and E. Alibo, 2003, Decreased price clustering in FTSE 100 futures contracts following a transfer from floor to electronic trading, Journal of Futures Markets 23, 647–659.
Chung, H. and S. Chiang, 2005, Price clustering in E-mini and floor-traded indexfutures, Journal of Futures Markets 26, 269–295.
Corwin, S. A. and P. Schultz, 2012,A simple way to estimate bid-ask spreads from daily high and low prices,The Journal of Finance 67, 719–760.
Fung, A. K.-W., D. M. Y. Mok and K. Lam, 2000, Intraday price reversals for index futures in theUS and Hong Kong, Journal of Banking and Finance24, 1179–1201.
Garbade, K. and Z. Lieber, 1977, On the independence of transactions on the New York Stock Exchange, Journal of Banking and Finance 1, 151–172.
Garman, M. B. and M. J. Klass, 1980,On the estimation of security price volatilities from historical data, Journal of Business 53, 67–78.
Grant, J. L., A. Wolf and S.Yu, 2005, Intraday price reversals in the US stockindex futures market: A 15-year study, Journal of Banking and Finance 29, 1311–1327.
Heston, S. L.,R.A.Korajczyk andR.Sadka, 2010, Intraday patterns in the cross-section of stock returns, The Journal of Finance 65, 1369–1407.
Laux, P. A. and A. J. Jr. Senchack, 1992, Bid-ask spreads in financial futures, Journal of Futures Markets12, 621–634.
Ohta, W., 2006, An analysis of intraday patterns in priceclustering on the Tokyo Stock Exchange,Journal of Banking and Finance 30, 1023–1039.
Parkinson, M., 1980,The extreme value method for estimating the variance of the rate of return, Journal of Business53, 61–65.
Rentzler, J., K. Tandon and S. Yu, 2006, Intraday price-reversal patterns in the currency futures market: The impact of the introduction of GLOBEX and the euro, Journal of Futures Markets 26, 1089–1130.
Roll, R., 1984,Asimple implicit measure of the effective bid-ask spread inanefficient market,The Journal of Finance 39, 1127–1140.
Schultz, P., 2000, Regulatory and legal pressures and the costs of NASDAQ trading, The Review of Financial Studies13, 917–957