Paper: arXiv 2404.11722

Abstract

This research extends the conventional concepts of the bid–ask spread (BAS) and mid-price to include the total market order book bid–ask spread (TMOBBAS) and the global mid-price (GMP). Using high-frequency trading data, we investigate these new constructs, finding that they have heavy tails and significant deviations from normality in the distributions of their log returns, which are confirmed by three different methods. We shift from a static to a dynamic analysis, employing the ARMA(1,1)-GARCH(1,1) model to capture the temporal dependencies in the return time-series, with the normal inverse Gaussian distribution used to capture the heavy tails of the returns. We apply an option pricing model to address the risks associated with the low liquidity indicated by the TMOBBAS and GMP. Additionally, we employ the Rachev ratio to evaluate the risk–return performance at various depths of the limit order book and examine tail risk interdependencies across spread levels. This study provides insights into the dynamics of financial markets, offering tools for trading strategies and systemic risk management.

Complexity vs Empirical Score

  • Math Complexity: 6.5/10
  • Empirical Rigor: 7.0/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper employs advanced mathematical models like ARMA-GARCH with Normal Inverse Gaussian distributions and applies option pricing theory, indicating high complexity. It uses high-frequency limit order book data from LOBSTER and analyzes three specific stocks, demonstrating strong empirical rigor.

Research Flowchart

  flowchart TD
  A["Research Goal<br>Define & Extend BAS/Mid-Price to TMOBBAS/GMP"] --> B["Data<br>High-Frequency Trading Data"]
  B --> C["Distribution Analysis<br>Test Normality & Heavy Tails<br>(3 Methods)"]
  C --> D["Dynamic Modeling<br>ARMA(1,1)-GARCH(1,1) + NIG Distribution"]
  D --> E["Risk Assessment<br>Option Pricing & Rachev Ratio"]
  E --> F["Outcomes<br>Tail Risk Interdependencies<br>Trading & Risk Management Tools"]

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0 of 52 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.