Paper: arXiv 2312.08927

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.

Complexity vs Empirical Score

  • Math Complexity: 7.5/10
  • Empirical Rigor: 8.0/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper employs advanced stochastic process modeling (Hawkes processes with compound distributions, inhibitory kernels, and spread constraints) and non-parametric calibration, indicating high math complexity. It is backed by detailed empirical data (NASDAQ Level 2 data, order size distributions, market impact studies) and model validation against baselines, showing high empirical rigor.

Research Flowchart

  flowchart TD
  A["Research Goal:<br>Model LOB Dynamics & Order Sizes<br>using Compound Hawkes Process"] --> B["Data Input:<br>NASDAQ Equity Stock LOB Data"]
  
  B --> C["Key Methodology:<br>Compound Hawkes Process<br>with Calibrated Order Size Distributions"]
  
  C --> D["Computational Process:<br>Non-parametric Calibration<br>with Time-of-Day Conditioning"]
  
  D --> E["Key Findings:<br>1. Novel Methodology<br>2. Validated Model Fits vs Baselines<br>3. Replicated Concave Market Impact"]

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6 of 105 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.