Semiparametric estimation of the bid-ask spread in extended roll models

We propose new methods for estimating the bid ask spread from observed transaction prices alone. Our methods are based on the empirical characteristic function. We compare our methods theoretically and numerically with the Roll (1984) method as well as with its best known competitor, the Hasbrouck (2004) method, and find that our estimators perform much better when this distribution is far from Gaussian. Our methods are applied to the E-mini futures contract on the S&P 500 during the Flash Crash of May 6, 2010. We also establish root T consistency and asymptotic normality of the proposed estimators in various extended Roll models. (C) 2018 Elsevier B.V. All rights reserved.