A New Effective Spread Estimator Based on Price Range

Abstract

This paper proposes an quasi maximum likelihood estimator (QMLE) for effective spread by approximating the distribution of the logarithm of price range with a normal distribution based on Roll’s price model and also investigates the statistical properties of the QMLE. Besides, Monte Carlo simulation studies have been conducted to make a comparison of the accuracy between the QMLE and other three estimators proposed in the early literature, namely Roll estimator (1984), the Bayesian estimator of Hasbrouck (2004) and the High-Low estimator of Corwin and Schultz (2012). Simulation results show that, both in the ideal case when the prices can be observed continuously and in the non-ideal case when trading inconsecutive, the QMLE and High-Low estimator are more accurate than the other two estimators. If the volatility is relatively smaller than the spread, the performance of QMLE will be superior to the High-Low method. Moreover, the QMLE is obviously more robust than the High-Low estimator in the non-ideal situation. Finally, an empirical study in Chinese stock markets also proves that the QMLEs performance is better than the other three estimators. Therefore, QMLE is an effective proxy for the transaction cost of financial assets.