Skip to content

Limit Order Book (LOB)

Definition

A Limit Order Book (LOB) is the real-time data structure used by electronic exchanges to record all outstanding buy and sell orders for an asset. It organises orders by price level and time priority, and the current state of the LOB represents the full supply and demand schedule for the asset at any instant.

Structure

The LOB has two sides: - Bid side — buy limit orders, ordered from highest to lowest price. The highest bid price is the best bid. - Ask side — sell limit orders, ordered from lowest to highest price. The lowest ask price is the best ask.

The bid-ask spread = best ask − best bid. The mid-price = (best bid + best ask) / 2.

Each price level contains a queue of orders (FIFO priority). The market depth at a level is the total quantity resting there.

Order types

Type Description
Limit order Rest in the book at a specified price until filled or cancelled
Market order Execute immediately against the best available prices
Cancellation Remove a resting limit order
Modification Change the quantity (and sometimes price) of a resting order

LOB as data

LOB data comes in two forms: - Full order-by-order (tick data) — every individual event (add, cancel, modify, trade) with nanosecond timestamps. - Snapshot data — periodic snapshots of the top \(N\) price levels (e.g., every second). Loses event-level detail.

LOBSTER (LOB System for NASDAQ data) is a common academic data source used in papers like deep-lob-forecasting.

Key empirical properties

Tick-size taxonomy (Briola et al. 2024)

Stocks behave differently depending on the ratio of mean spread \(\langle\sigma\rangle\) to tick size \(\theta\):

Regime Condition Empirical profile
Small-tick \(\langle\sigma\rangle \gtrsim 3\theta\) Wide, heavy-tailed spread distribution; thin queues; hardest to forecast
Medium-tick \(1.5\theta \lesssim \langle\sigma\rangle \lesssim 3\theta\) "Borderline" — mixed behaviour (AAPL ≈ large-tick; ABBV/PM ≈ small-tick)
Large-tick \(\langle\sigma\rangle \lesssim 1.5\theta\) Spread pinned near 1 tick; deep queues; queues shrink before transactions (directional leak); most forecastable

This taxonomy is the strongest single predictor of whether a DL model will work on a given stock — see deep-lob-forecasting.

Open questions

  • How much of the LOB signal is genuine informed flow vs noise from high-frequency market makers?
  • What is the right level of the book to model? Best bid/ask vs multi-level?
  • How do LOB dynamics change under different market regimes (normal, stressed, flash crash)?

Simulation and modelling

Interactive LOB simulators are essential for backtesting, execution benchmarking, and strategy stress-testing: - Zero-intelligence models (Smith et al. 2003; Cont–De Larrard 2013) — constant-rate arrivals, fit first-order statistics only. - Queue-Reactive (QR) model (Huang et al. 2015) — event intensities conditioned on queue state; see queue-reactive-model. - Extended QR — reality-gap-lob-simulation adds state projection onto (imbalance, spread), non-exponential inter-event times capturing latency-race bursts, and power-law impact feedback so post-execution dynamics are realistic.

Connections