Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Limit Order Book Dynamics and Order Size Modelling Using Compound Hawkes Process

Konark Jain, Nick Firoozye, Jonathan Kochems, Philip Treleaven

TL;DR

This work advances limit order book modeling by introducing a $d$-dimensional Compound Hawkes Process (CHP) that integrates stochastic order sizes drawn from calibrated distributions, while enforcing a non-negative spread and incorporating time-of-day effects. It combines a six-queue, 12-event-type structure with spread-dependent intensities and a price-dynamics mechanism, and uses enhanced non-parametric calibration to allow inhibitory cross-excitations. The authors validate the approach on NASDAQ Apple data, demonstrate accurate replication of stylized facts, and show a concave market-impact response to meta-orders, outperforming Poisson baselines and certain Hawkes variants. The resulting CHP-based simulator yields a realistic, tunable framework for market microstructure analysis and market-impact experimentation with practical implications for execution strategies and risk management.

Abstract

Hawkes Process has been used to model Limit Order Book (LOB) dynamics in several ways in the literature however the focus has been limited to capturing the inter-event times while the order size is usually assumed to be constant. We propose a novel methodology of using Compound Hawkes Process for the LOB where each event has an order size sampled from a calibrated distribution. The process is formulated in a novel way such that the spread of the process always remains positive. Further, we condition the model parameters on time of day to support empirical observations. We make use of an enhanced non-parametric method to calibrate the Hawkes kernels and allow for inhibitory cross-excitation kernels. We showcase the results and quality of fits for an equity stock's LOB in the NASDAQ exchange and compare them against several baselines. Finally, we conduct a market impact study of the simulator and show the empirical observation of a concave market impact function is indeed replicated.

Limit Order Book Dynamics and Order Size Modelling Using Compound Hawkes Process

TL;DR

This work advances limit order book modeling by introducing a -dimensional Compound Hawkes Process (CHP) that integrates stochastic order sizes drawn from calibrated distributions, while enforcing a non-negative spread and incorporating time-of-day effects. It combines a six-queue, 12-event-type structure with spread-dependent intensities and a price-dynamics mechanism, and uses enhanced non-parametric calibration to allow inhibitory cross-excitations. The authors validate the approach on NASDAQ Apple data, demonstrate accurate replication of stylized facts, and show a concave market-impact response to meta-orders, outperforming Poisson baselines and certain Hawkes variants. The resulting CHP-based simulator yields a realistic, tunable framework for market microstructure analysis and market-impact experimentation with practical implications for execution strategies and risk management.

Abstract

Hawkes Process has been used to model Limit Order Book (LOB) dynamics in several ways in the literature however the focus has been limited to capturing the inter-event times while the order size is usually assumed to be constant. We propose a novel methodology of using Compound Hawkes Process for the LOB where each event has an order size sampled from a calibrated distribution. The process is formulated in a novel way such that the spread of the process always remains positive. Further, we condition the model parameters on time of day to support empirical observations. We make use of an enhanced non-parametric method to calibrate the Hawkes kernels and allow for inhibitory cross-excitation kernels. We showcase the results and quality of fits for an equity stock's LOB in the NASDAQ exchange and compare them against several baselines. Finally, we conduct a market impact study of the simulator and show the empirical observation of a concave market impact function is indeed replicated.
Paper Structure (21 sections, 20 equations, 17 figures)

This paper contains 21 sections, 20 equations, 17 figures.

Table of Contents

  1. Introduction
  2. Empirical Distributions of Order Sizes:
  3. Properties of the Order Book Dynamics:
  4. Related Work
  5. Methodology
  6. Mathematical Formulation:
  7. Calibration:
  8. Results
  9. Calibration for Simulated Data:
  10. Calibration for Equities LOB:
  11. Calibration of Order Size Distributions
  12. Quality of fit metrics:
  13. Comparison to a similar Poisson Process formulation:
  14. The effect of mis-specifying the order size distribution:
  15. Comparison with Other Hawkes Process Models:
  16. ...and 6 more sections

Figures (17)

  • Figure 1: Empirical Distribution of Order Sizes
  • Figure 2: Order Book Snapshot
  • Figure 3: Simulated Data Calibration
  • Figure 4: Intensities conditioned by Time of Day : we report the average number of events per 30 min bin in a 6 month period
  • Figure 5: Excitation Kernels
  • ...and 12 more figures