A continuous and efficient fundamental price on the discrete order book grid

TL;DR

This paper introduces a model for fundamental prices in discrete order books, incorporating quote discretization and rebates, validated with high-frequency Nasdaq data, and proposes an improved estimator for the fundamental price.

Contribution

It adapts the Madhavan, Richardson, and Roomans model to realistic order books with discretization and rebates, providing a new estimator for the fundamental price.

Findings

Model predictions confirmed with empirical data

Rebate-adjusted volume imbalance improves fundamental price estimation

Proposed estimator outperforms simpler alternatives

Abstract

This paper develops a model of liquidity provision in financial markets by adapting the Madhavan, Richardson, and Roomans (1997) price formation model to realistic order books with quote discretization and liquidity rebates. We postulate that liquidity providers observe a fundamental price which is continuous, efficient, and can assume values outside the interval spanned by the best quotes. We confirm the predictions of our price formation model with extensive empirical tests on large high-frequency datasets of 100 liquid Nasdaq stocks. Finally we use the model to propose an estimator of the fundamental price based on the rebate adjusted volume imbalance at the best quotes and we empirically show that it outperforms other simpler estimators.