Exact Hurst exponent and crossover behavior in a limit order market model

TL;DR

This paper models a limit order market using an exclusion particle model, revealing a crossover in price behavior from over-diffusion to normal diffusion, with exact Hurst exponent results and insights into universality and scaling properties.

Contribution

It introduces an exclusion process model that exactly predicts the Hurst exponent and crossover behavior in limit order markets, supported by analytical and numerical evidence.

Findings

Exact Hurst exponent H=2/3 for early times

Crossover from over-diffusion to diffusion behavior

Scaling property of the Hurst plot in the crossover regime

Abstract

An exclusion particle model is considered as a highly simplified model of a limit order market. Its price behavior reproduces the well known crossover from over-diffusion (Hurst exponent H>1/2) to diffusion (H=1/2) when the time horizon is increased, provided that orders are allowed to be canceled. For early times a mapping to the totally asymmetric exclusion process yields the exact result H=2/3 which is in good agreement with empirical data. The underlying universality class of the exclusion process suggests some robustness of the exponent with respect to changes in the trading rules. In the crossover regime the Hurst plot has a scaling property where the bulk deposition/cancellation rate is the critical parameter. Analytical results are fully supported by numerical simulations.