Do Round Numbers Hold Prices? Occupation Densities and Depth-Conditioned Hazards in the Limit Order Book

Paper: arXiv 2610.34787

Authors: Jiwon Jung, Kiseop Lee

Abstract

Prices cluster at round numbers, a pattern often interpreted as evidence that these levels act as price barriers. This pattern also admits a mechanical explanation: more liquidity rests there, and prices take longer to leave deeper queues. Limit order book data allow us to distinguish these mechanisms through a tick-grid framework in which local time counts departures and level-wise volatility reflects the departure hazard. Using data for five Nasdaq stocks throughout 2025, we find that round levels attract more liquidity but do not exhibit longer depth-adjusted durations. Intel and SoFi show directional effects, with departures biased away from round levels.

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 novel tick-grid framework using local time and duration analysis to investigate price clustering, offering a sophisticated statistical approach to a well-known market microstructure phenomenon. It combines advanced mathematical concepts with rigorous empirical testing on high-frequency LOB data, providing strong evidence against the ‘price barrier’ hypothesis for round numbers after adjusting for liquidity.

Research Flowchart

  flowchart TD
    A[Research Goal: Do Round Numbers Hold Prices?] --> B{Methodology: Tick-Grid Framework};
    B --> C[Inputs: LOB Data for 5 Nasdaq Stocks (2025)];
    C --> D{Computational Processes: Local Time, Level-wise Volatility, Departure Hazard};
    D --> E[Outcome 1: Round Levels Attract More Liquidity];
    D --> F[Outcome 2: No Longer Depth-Adjusted Durations at Round Levels];
    F --> G[Outcome 3: Intel/SoFi Show Directional Effects (Departures Biased Away from Round Levels)];