The LimitOrder Book as a Queue-Based Price Formation Mechanism

Abstract This paper presents a mechanical description of price formation in limit order books (LOB), treating them as queue-based matching systems rather than abstract price-discovery mechanisms. Operating under discrete tick sizes and FIFO queue priority, price movements occur only when queues at the best bid or ask are fully depleted—a structural outcome of the continuous double auction rules, independent of trader intent or information asymmetry. The analysis introduces the A-B-C-D framework, classifying all market interactions into four primitive actions: aggressive buy, passive sell, aggressive sell, and passive buy. These roles form complementary pairs and circulate continuously as agents enter and exit positions. Inventory exposure determines directional preference mechanically, while order choice—limit, market, or cancellation—links incentives to price impact. Key mechanical phenomena examined include: queue formation, depletion, and replenishment; the role of cancellations as negative depth shocks that deteriorate execution prices without generating trades; iceberg orders as endogenous price stabilizers that delay queue exhaustion while concentrating inventory; and the "fill-flip" mechanism, where passive liquidity providers are forced to become aggressive takers under inventory constraints. A detailed analysis of one-tick price transitions reveals how queue composition is entirely reconstructed after a price move, with agents in loss reinforcing the new bid level through defensive limit orders—creating persistence without new information. The paper concludes that directional pressure emerges endogenously from queue-level incentives and role transitions under inventory constraints, not from heterogeneous beliefs or informational advantages. All results follow directly from LOB mechanics and require no assumptions about trader psychology, strategy, or market manipulation.