Simple model of a limit order-driven market

TL;DR

This paper presents a minimalistic limit order market model where traders randomly choose between market and limit orders, successfully reproducing realistic market features like fat tails, volatility correlations, and complex Hurst exponents.

Contribution

The paper introduces a simple, stochastic limit order market model that captures key statistical features of real financial markets without strategic behavior.

Findings

Reproduces fat-tailed price fluctuation distributions

Displays long-range volatility correlations

Shows non-trivial Hurst exponent in price signals

Abstract

We introduce and study a simple model of a limit order-driven market. Traders in this model can either trade at the market price or place a limit order, i.e. an instruction to buy (sell) a certain amount of the stock if its price falls below (raises above) a predefined level. The choice between these two options is purely random (there are no strategies involved), and the execution price of a limit order is determined simply by offsetting the most recent market price by a random amount. Numerical simulations of this model revealed that despite such minimalistic rules the price pattern generated by the model has such realistic features as ``fat'' tails of the price fluctuations distribution, characterized by a crossover between two power law exponents, long range correlations of the volatility, and a non-trivial Hurst exponent of the price signal.