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

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.