Hydrodynamic limit of order book dynamics

TL;DR

This paper derives a fluid limit for a Markov order book model, showing convergence to deterministic processes and validating the approximation with empirical data for liquid stocks.

Contribution

It introduces a novel fluid limit for two-sided order book dynamics and demonstrates its empirical relevance for liquid stocks.

Findings

The measure-valued processes converge to deterministic limits.

The fluid approximation fits well for liquid stocks during certain periods.

Empirical validation supports the theoretical model.

Abstract

In this paper, we establish a fluid limit for a two--sided Markov order book model. Our main result states that in a certain asymptotic regime, a pair of measure-valued processes representing the "sell-side shape" and "buy-side shape" of an order book converges to a pair of deterministic measure-valued processes in a certain sense. We also test our fluid approximation on data. The empirical results suggest that the approximation is reasonably good for liquidly--traded stocks in certain time periods.