SignalTrace

Limit Order Book

John Montgomery4 min read

Limit Order Book

A limit order book (LOB) is the data structure and matching mechanism of modern electronic exchanges. It records all outstanding bid and ask limit orders at each price level and matches incoming market orders against them by price-time priority — best price first, and among orders at the same price, the one that arrived earliest (front of queue) fills first. Every event — a limit order posted, a limit order cancelled, a market order executed — changes the book. The LOB appears in this vault because it is the concrete trading environment for MDP-based Optimal Execution and Market Making models: it is what a Markov Decision Process Trading Model state vector tries to summarise, and what a Reinforcement Learning Trading Policy agent interacts with.

In MDP/RL terms the LOB supplies the state features (best bid/ask, depth at each level, order-book imbalance, spread, recent trade flow) and the transition dynamics (how the book evolves given the agent’s order and incoming flow). The classical Avellaneda-Stoikov 2008 market-making model abstracts the LOB into two ingredients: a Brownian-motion mid-price and Poisson order-arrival intensities λ(δ) = A·exp(−k·δ) that decay with quote distance from the mid-price. This abstraction is analytically convenient — it makes the dealer’s control problem solvable as a Hamilton-Jacobi-Bellman PDE — but it is a strong simplification of the real book.

Limit Order Book [part-of] Market Making Markov Decision Process Trading Model [trades_market] Limit Order Book Avellaneda-Stoikov 2008 [relates] Limit Order Book

The central tension this vault investigates is sharpest here: real LOB dynamics are non-Markovian, which contradicts the memoryless state an MDP requires. Lalor Swishchuk 2025 stress that “many studies have shown that LOB dynamics often follow non-Markovian properties” — the book “often experiences jumps, i.e., points of discontinuity,” and models “that can portray a dependency in past trade transactions are superior” to memoryless diffusion models. Empirical microstructure work confirms this: order arrivals, cancellations and trades cluster in time and excite one another across the buy and sell sides, which is why Hawkes Process models — self-exciting point processes whose intensity depends on the entire past event stream — fit real order flow far better than independent Poisson arrivals. A pure Hawkes-driven book is non-Markovian by construction; the decision-relevant future depends on history a finite state vector cannot encode. This is the Partial Observability / Non-Stationarity problem at the microstructure level.

Hawkes Process [contradicts] Limit Order Book Lalor Swishchuk 2025 [trades_market] Limit Order Book Limit Order Book [relates] Partial Observability

Two further LOB realities are routinely omitted from backtests and inflate reported results. First, trading happens at the bid and ask, not the mid-price: simulating fills at a constant-spread mid-price is, as Lalor Swishchuk 2025 note, “highly unrealistic in certain markets.” Second, price-time priority means queue position matters — a posted order does not fill until the queue ahead of it clears — yet most HFT literature “assume[s] that orders are automatically at the front of the queue.” Combined with the omission of Adverse Selection (informed counterparties), these simplifications produce the “large phantom gains” the paper warns about. The LOB is therefore both the natural home of MDP trading models and the level at which their convenient assumptions break down: any LOB-based market-making or execution backtest should be graded on whether it models bid/ask fills, queue position and adverse selection — most do not.

Limit Order Book [causes] Phantom Gains in Backtests Adverse Selection [part-of] Limit Order Book

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