The self-exciting nature of the bid-ask spread dynamics

Paper: arXiv 2303.02038

Authors: Ruihua Ruan, Emmanuel Bacry, Jean-François Muzy

Abstract

The bid-ask spread, which is defined by the difference between the best selling price and the best buying price in a Limit Order Book at a given time, is a crucial factor in the analysis of financial securities. In this study, we propose a “State-dependent Spread Hawkes model” (SDSH) that accounts for various spread jump sizes and incorporates the impact of the current spread state on its intensity functions. We apply this model to the high-frequency data from the Cac40 Euronext market and capture several statistical properties, such as the spread distributions, inter-event time distributions, and spread autocorrelation functions. We illustrate the ability of the SDSH model to forecast spread values at short-term horizons.

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 presents a mathematically sound extension of Hawkes processes (SDSH) tailored to limit order book spread dynamics, supported by solid empirical validation on high-frequency CAC40 data. It effectively captures market microstructure nuances, though full reproducibility is slightly constrained by proprietary high-frequency data requirements.

Research Flowchart

  flowchart TD
    A["Research Goal:<br>Model Self-Exciting Dynamics of Bid-Ask Spread"] --> B["Data Input:<br>Cac40 Euronext High-Frequency Data"]
    B --> C["Methodology:<br>Develop State-dependent Spread Hawkes Model (SDSH)"]
    C --> D["Computational Process:<br>Incorporate Jump Sizes & Spread State Effects"]
    D --> E["Model Calibration:<br>Fit Intensity Functions & Calculate Autocorrelations"]
    E --> F["Outcomes:<br>Capture Spread Distributions & Short-term Forecasting"]