Liquidity and Impact in Fair Markets

TL;DR

This paper introduces a theoretical framework for fair market prices based on market making strategies, linking spread and order impact, and validates it with empirical tests.

Contribution

It develops a general theory of fair prices applicable to any market satisfying a no-arbitrage condition, connecting impact and spreads.

Findings

Fair price corresponds to average liquidation value of infinitesimal stock units.

Spread is linked to the impact of market orders on the fair price.

Empirical tests support the theoretical predictions.

Abstract

We develop a theory which applies to any market dynamics that satisfy a fair market assumption on the nullity of the average profit of simple market making strategies. We show that for any such fair market, there exists a martingale fair price which corresponds to the average liquidation value (at the ask or the bid) of an infinitesimal quantity of stock. We show that this fair price is a natural reference price to compute the ex post gain of limit orders. Using only the fair market assumption, we link the spread to the impact of market orders on the fair price. We use our definition of the fair price to build empirical tests of the relevance of this notion whose results are consistent with our theoretical predictions.