Asymptotic comparison of three spread estimators based on Roll’s model

Abstract

In this paper we theoretically investigate the statistical properties of three popular bid–ask spread estimators, i.e., the covariance estimator of Roll (1984), the High–Low (HL) estimator based on daily high and low prices developed by Corwin and Schultz (2012) and the Close–High–Low (CHL) estimator recently proposed by Abdi and Ranaldo (2017). The biases and mean squared errors (MSE) of these three estimators have been derived and compared with each other asymptotically, which reveals explicitly the superior performance of HL and CHL estimators over Roll’s estimator. Moreover, if the volatility is relatively small compared to the spread, the performance of the CHL estimator is superior to the HL method. Then the subsequent simulation studies and bootstrap analysis on empirical examples also verify the theoretical results. The comparison method discussed here is different from the existing literature, which usually resorts to the correlation between the bid–ask spread estimators with a benchmark calculated from high-frequency data as they compare the performance of different estimators.