Modelling intensities of order flows in a limit order book

TL;DR

This paper introduces a new parametric model for simulating limit order books, capturing the dynamics of order submissions and cancellations with state-dependent intensities and a novel 'priority index' concept.

Contribution

The paper presents innovative functional forms for order flow intensities and a new model for cancellations, enhancing the realism of limit order book simulations.

Findings

Model accurately replicates empirical order flow patterns

Outperforms standard Poisson models in simulations

Provides detailed insights into order cancellation mechanisms

Abstract

We propose a parametric model for the simulation of limit order books. We assume that limit orders, market orders and cancellations are submitted according to point processes with state-dependent intensities. We propose new functional forms for these intensities, as well as new models for the placement of limit orders and cancellations. For cancellations, we introduce the concept of "priority index" to describe the selection of orders to be cancelled in the order book. Parameters of the model are estimated using likelihood maximization. We illustrate the performance of the model by providing extensive simulation results, with a comparison to empirical data and a standard Poisson reference.