Feedback and efficiency in limit order markets

TL;DR

This paper proposes a consistency criterion for price impact functions in limit order markets, emphasizing the importance of bid-ask spread and order feedback to prevent arbitrage, with empirical validation on Paris Stock Exchange stocks.

Contribution

Introduces a new consistency criterion for price impact functions that accounts for order feedback and bid-ask spread, ensuring no arbitrage at small time scales.

Findings

All stocks in Paris Stock Exchange studied have consistent price impact functions.

The proposed criterion effectively prevents chain arbitrage exploitation.

Feedback mechanisms are crucial for market stability at high frequency.

Abstract

A consistency criterion for price impact functions in limit order markets is proposed that prohibits chain arbitrage exploitation. Both the bid-ask spread and the feedback of sequential market orders of the same kind onto both sides of the order book are essential to ensure consistency at the smallest time scale. All the stocks investigated in Paris Stock Exchange have consistent price impact functions.