Estimation of bid-ask spreads in the presence of serial dependence

TL;DR

This paper develops and compares new moment-based estimators for bid-ask spreads considering serial dependence in prices and microstructure noise, improving accuracy over existing methods.

Contribution

It introduces novel estimators for bid-ask spreads under serial dependence, extending basic models to more realistic fractional Brownian motion and Ornstein-Uhlenbeck processes.

Findings

Estimators are consistent and asymptotically normal.

Compared favorably with existing approaches on simulated data.

Enhanced modeling of serial dependence improves spread estimation accuracy.

Abstract

Starting from a basic model in which the dynamic of the transaction prices is a geometric Brownian motion disrupted by a microstructure white noise, corresponding to the random alternation of bids and asks, we propose moment-based estimators along with their statistical properties. We then make the model more realistic by considering serial dependence: we assume a geometric fractional Brownian motion for the price, then an Ornstein-Uhlenbeck process for the microstructure noise. In these two cases of serial dependence, we propose again consistent and asymptotically normal estimators. All our estimators are compared on simulated data with existing approaches, such as Roll, Corwin-Schultz, Abdi-Ranaldo, or Ardia-Guidotti-Kroencke estimators.