Electronic Markets from First Principles

Market structure, microstructure, execution, and realistic simulation.

Status Curriculum framingApproach Mechanics before models

An electronic market is simultaneously a rule system, a distributed event stream, an economic mechanism, and an environment in which participants act with incomplete information.

This book develops those layers in that order. It begins with the concrete mechanics of orders and trades, then explains liquidity and order flow, execution and market making, empirical evidence, simulation, risk, and finally the mathematical models that compress those observations.

Every chapter should answer five questions:

What observable market phenomenon are we trying to explain?
Which exchange rules and participant constraints produce it?
What data would distinguish competing explanations?
Which assumptions does the model make?
What would make a simulation or conclusion misleading?

This is not primarily a low-latency programming book. Its companion, Computer Science from First Principles, covers data structures, machine behavior, operating systems, concurrency, networking, and performance engineering. This book uses that machinery only when implementation details change market meaning or experimental validity.

Start with why markets exist, inspect the full curriculum, or use the source map to connect chapters with external books and laboratories.

Curriculum

The path is deliberately causal:

rules and participants
        ↓
observable order-book behavior
        ↓
execution and market-making decisions
        ↓
data, estimation, and simulation
        ↓
risk controls and mathematical models

Mechanics

Learn what orders mean, how venues organize trading, how matching rules determine outcomes, and which direct costs accompany a trade.

Market microstructure

Explain spreads, depth, liquidity, order flow, queue position, adverse selection, price discovery, and impact from participant incentives and market rules.

Execution

Turn a desired position change into an explicit execution objective, cost benchmark, schedule, order policy, and routing decision.

Market making

Study quoting as a coupled inventory, adverse-selection, fill-probability, and control problem—not as a guaranteed spread-capture strategy.

Data and empirical work

Establish event-time semantics, reconstruct trustworthy state, measure stylized facts, estimate parameters, and separate statistical evidence from artifacts.

Simulation and backtesting

Build event-driven experiments with honest information boundaries, queue and fill models, latency, transaction costs, and sensitivity analysis.

Risk and operations

Track positions and exposure, enforce limits, reconcile external state, handle uncertainty, and define safe behavior during failures or regime changes.

Mathematical models

Introduce probability, point processes, stochastic processes, optimization, and control only after the market mechanisms and observables they model are understood.

The first six parts form the main learning path. Risk accompanies every experiment. Mathematical chapters are optional on a first pass and become essential for deeper research.

Source Map

No single reference is the authority for every layer of electronic markets. The book should use primary venue specifications and empirical papers where exact rules or claims matter, while relying on broader texts for durable models.

Market mechanics

Larry Harris’s Trading and Exchanges supplies the institutional vocabulary: participants, orders, market structures, liquidity, dealers, and trading problems. It belongs near the beginning because later models assume this language.

The working edition is Larry Harris, Trading and Exchanges: Market Microstructure for Practitioners, Oxford University Press, ISBN 978-0-19-514470-3. See the Harris reading map for the chapters assigned to each part of this book and the historical details that require newer primary sources.

Thierry Foucault, Marco Pagano, and Ailsa Röell’s Market Liquidity: Theory, Evidence, and Policy supplies the complementary theoretical and empirical treatment of liquidity, price discovery, order flow, trade size, limit order books, fragmentation, and transparency. See the Foucault–Pagano–Röell reading map.

Graduate microstructure models

The MTH9879 Market Microstructure Models materials provide exercises and models for order flow, spreads, inventory-based market making, impact, execution, latency, and routing. They are best treated as advanced laboratories after the mechanics are clear.

Realistic replay

hftbacktest is a practical laboratory for queue position, latency, L2/L3 books, fill assumptions, imbalance signals, and tick replay. Its results are conditional on its market, latency, queue, and impact models; those assumptions must remain visible.

Mathematical depth

Cartea, Jaimungal, and Penalva’s Algorithmic and High-Frequency Trading supports the later treatment of market making, optimal execution, stochastic models, and control.

Systems companions

CPU-performance, modern-hardware-algorithm, and Rust-performance references belong primarily to Computer Science from First Principles. They should be cited here only where implementation changes timestamps, queue position, experiment validity, or operational behavior.

Source rule

A repository is a laboratory, not proof that a market rule is universal or a model is realistic. Every experiment should identify:

The venue and period represented by the data.
The matching and priority rules assumed.
The observable information available to the strategy.
The latency, fill, fee, and impact models.
The claim the experiment can and cannot support.

Edition rule

The working Foucault–Pagano–Röell file is the 2013 first edition, not the expanded 2023 second edition. Its foundational models remain useful, but claims about modern algorithms, venue structure, regulation, and empirical conditions require newer sources.

Harris Reading Map

Source Larry HarrisRole Foundational reference

Larry Harris, Trading and Exchanges: Market Microstructure for Practitioners. Oxford University Press. ISBN 978-0-19-514470-3.

Harris provides the institutional vocabulary for the first half of this book. Its greatest strengths are the distinctions among participant motives, order properties, market structures, liquidity demand and supply, spreads, trading costs, and market quality.

It should guide our explanations without dictating our organization. Our book will begin with smaller interactive mechanisms, incorporate later empirical work, and distinguish contemporary electronic-market rules from durable principles.

Primary reading path

Our part	Harris chapters	Purpose
Market Mechanics	3–9	Trading industry, orders, market structures, order-driven markets, brokers, motives, and good markets
Market Microstructure	10–14, 19–20	Information, anticipation, manipulation, dealers, spreads, liquidity, and volatility
Execution	4, 7, 18, 21–22	Order properties, agency, buy-side trading, transaction costs, and performance evaluation
Market Making	10, 13–14, 19–20	Informed trading, dealer behavior, spread components, liquidity, and volatility
Data and Empirical Work	20–22	Volatility, liquidity measurement, transaction costs, and evaluation
Risk and Operations	7, 22, 28–29	Agency, evaluation, circuit breakers, and information boundaries

The mathematical-model and simulation parts require later sources. Harris supplies motivations and definitions for those chapters, but not a modern event-driven backtesting or stochastic-control treatment.

Chapter-level assignments

Mechanics

Chapter 3, The Trading Industry → participants, intermediaries, venues, and industry roles.
Chapter 4, Orders and Order Properties → order instructions, tradeoffs, and order choice.
Chapter 5, Market Structures → dealer, auction, brokered, and crossing mechanisms.
Chapter 6, Order-driven Markets → books, priority, and order interaction.
Chapter 7, Brokers → agency, routing, conflicts, and execution responsibility.
Chapter 8, Why People Trade → participant objectives and gains from trade.
Chapter 9, Good Markets → liquidity, price discovery, fairness, and market quality.

Microstructure and liquidity supply

Chapter 10, Informed Traders and Market Efficiency → information, prices, and adverse selection.
Chapter 11, Order Anticipators → prediction of other participants’ demand.
Chapter 12, Bluffers and Market Manipulation → strategic signaling and deceptive order flow.
Chapter 13, Dealers → liquidity supply, inventory, and dealer economics.
Chapter 14, Bid/Ask Spreads → spread components and measurement.
Chapters 15–18 → block, value, arbitrage, and buy-side trading motives.
Chapter 19, Liquidity → dimensions, origins, and beneficiaries of liquidity.
Chapter 20, Volatility → price variation and its relationship to trading.

Measurement and design

Chapter 21, Liquidity and Transaction Cost Measurement → spread and execution-cost concepts.
Chapter 22, Performance Evaluation and Prediction → benchmarks, attribution, and the difficulty of evaluating skill.
Chapters 23–27 → index markets, specialists, internalization, fragmentation, competition, and automated trading.
Chapter 28, Bubbles, Crashes, and Circuit Breakers → instability and intervention.
Chapter 29, Insider Trading → information boundaries and market integrity.

Durable concepts versus historical details

Treat these as durable conceptual foundations:

Participants trade for different reasons and under different constraints.
Every order type exchanges one risk for another.
Market structure affects execution, information revelation, and liquidity.
Liquidity has several dimensions and is costly to supply.
Spreads compensate for costs and risks rather than representing free profit.
Trading-cost and performance measurements depend on their benchmark.

Treat these as historical context until verified against current primary sources:

Named venues, intermediaries, and industry roles.
Available order types and precedence rules.
Fee schedules, tick sizes, lot sizes, and trading hours.
Market-data contents and timestamp semantics.
Routing, best-execution, disclosure, and market-integrity obligations.
Claims about the relative importance of floor, dealer, crossing, and automated markets.

For current facts, the eventual chapter should cite the relevant exchange rulebook, technical specification, regulator, or dated empirical study.

Writing rule

Use Harris to establish vocabulary and causal questions. Then ask:

Can the mechanism be demonstrated with a smaller interactive market?
Which parts are universal and which depend on a venue rule?
What observable data would test the explanation?
What has changed since the book’s publication?
Which later source supplies the empirical or mathematical extension?

Foucault–Pagano–Röell Reading Map

Source Foucault, Pagano, and RöellEdition First (2013)Role Liquidity and price formation

Thierry Foucault, Marco Pagano, and Ailsa Röell, Market Liquidity: Theory, Evidence, and Policy. Oxford University Press, 2013. ISBN 978-0-19-993624-3. DOI 10.1093/acprof:oso/9780199936243.001.0001.

This source complements Harris. Harris gives us participant motives and institutional vocabulary; Foucault, Pagano, and Röell give us models and evidence for the trading process itself—especially liquidity, price discovery, order flow, trade size, the limit order book, fragmentation, and transparency.

The supplied file is the 2013 first edition. It is suitable for the foundational chapters below. A later revision should consult the 2023 second edition and current venue specifications for algorithmic trading, high-frequency market making, fragmentation, regulation, and recent evidence.

Primary reading path

Our part	Source chapters	Purpose
Market Mechanics	Introduction; 1	Why real trading differs from frictionless exchange; dealer and auction mechanisms; trading rules
Market Microstructure	Introduction; 2–4; 6–8	Liquidity measurement, order flow, depth, limit order books, fragmentation, and transparency
Execution	2; 4; 6–7	Trading costs, trade size, order choice, venue choice, and execution conditions
Market Making	3–4; 6	Price dynamics, inventory absorption, depth, and limit-order supply
Data and Empirical Work	2–5	Liquidity measures, empirical price dynamics, depth, and estimation
Mathematical Models	3–4; 6–9	Order-flow models, trade-size models, equilibrium liquidity, and asset-pricing implications

Chapter-level assignments

Introduction → the gap between frictionless asset-pricing models and real trading; market liquidity; price discovery; the interaction of market, funding, and monetary liquidity.
Chapter 1, Trading Mechanics and Market Structure → rules of the game, dealer markets, continuous limit order books, call auctions, hybrid structures, and transparency.
Chapter 2, Measuring Liquidity → spreads, price impact, execution costs, and the limits of any single liquidity statistic.
Chapter 3, Order Flow, Liquidity, and Securities Price Dynamics → informed and uninformed order flow, price response, and liquidity provision.
Chapter 4, Trade Size and Market Depth → quantity, depth, and price concessions.
Chapter 5, Estimating the Determinants of Market Illiquidity → empirical identification and estimation.
Chapter 6, Limit Order Book Markets → endogenous order choice and liquidity supply in a book.
Chapter 7, Market Fragmentation → competition, concentration, and venue choice.
Chapter 8, Market Transparency → displayed information and participant behavior.
Chapter 9, Liquidity and Asset Prices → liquidity premia and funding-liquidity feedback.
Chapter 10, Liquidity, Price Discovery, and Corporate Policies → consequences beyond the trading desk.

How we will use it

This book will not copy the source’s chapter order. Each chapter starts with an observable mechanism, then introduces the smallest model needed to explain it. The source provides hypotheses and modeling discipline; current exchange specifications and empirical papers must establish contemporary facts.

For each borrowed model, state:

Which participants are present.
What each participant knows and observes.
What actions the mechanism permits.
How and when orders meet.
Which quantity the model predicts.
What real-world feature the model deliberately leaves out.

First-edition boundary

Treat the first edition as authoritative for durable definitions and foundational mechanisms, not for the current state of electronic markets. The following always need newer verification:

Venue ownership, market share, and trading protocols.
Order types, matching rules, and transparency regimes.
Tick sizes, fees, access, and market-data products.
The prevalence and effects of high-frequency and algorithmic trading.
Regulatory requirements and market-design reforms.
Quantitative claims tied to a particular sample or historical episode.

Market Mechanics

Status DraftPurpose Establish the rules

Before modeling a market, learn what its participants can submit, how a venue processes those instructions, and what constitutes an execution.

This part remains descriptive before becoming mathematical. Exact rules vary by venue, instrument, jurisdiction, and time, so concrete claims should eventually cite the relevant specification.

Why Markets Exist

A market is not merely a place where trades happen. It is a mechanism for finding counterparties, forming prices, and deciding who trades, when, and on what terms.

Part Market MechanicsModel One asset, six participantsGoal Separate gains from trade from market design

The six participants above want to trade the same asset, one unit each. A buyer’s number is the most they would pay. A seller’s number is the least they would accept. The potential gain from a particular trade is:

gain from trade = buyer's value - seller's cost

If the difference is positive, some price can make both sides willing to trade. The mechanism does not create that gain. It determines whether the two sides find each other, how long they wait, what they learn, and how the gain is divided.

That distinction is the foundation of market microstructure:

The desire to exchange explains why a market can exist. The trading mechanism explains what actually happens.

Exchange begins with disagreement

People trade because the same asset can serve them differently.

A buyer may value an asset because it moves purchasing power into the future, hedges a risk, completes a portfolio, supplies an input, or expresses information about future prices. A seller may want cash now, less exposure, a different asset, or a chance to act on opposing information. Participants can also differ in constraints, inventories, tax positions, funding, and time horizons.

Harris groups these motives into broad families: investment and borrowing, asset exchange, hedging and risk sharing, speculation, dealing, and other non-investment motives. One participant can have several motives at once. The important lesson is not the taxonomy itself; it is that order flow is heterogeneous. A buy order does not tell you, by itself, why the buyer wants to trade. [Harris, ch. 8]

This heterogeneity creates gains from trade. Suppose a buyer values one unit at 106 and a seller values keeping it at 94. Any price between them can make both better off:

buyer surplus  = 106 - price
seller surplus = price - 94
total surplus  = 106 - 94 = 12

The price divides the surplus. It does not determine the total surplus for that buyer–seller pair.

Why bilateral search is not enough

Two people can trade without an exchange, dealer, or order book. They must still solve several problems:

Discovery: Who is willing to take the other side?
Comparison: Is this the best available counterparty and price?
Negotiation: What price and quantity are acceptable?
Timing: Will the counterparty still be available when needed?
Credibility: Can each side trust the other’s instructions and ability to settle?
Information: Does the other side know something important?

Bilateral search can be appropriate for unusual, large, or highly negotiable transactions. It becomes expensive when many participants repeatedly trade a standardized instrument. Every trader would otherwise have to rediscover counterparties and terms.

An organized market reduces these coordination costs. It standardizes messages and contracts, concentrates or connects trading interest, publishes some information, defines how orders receive priority, and supplies procedures for execution and settlement.

What a trading mechanism decides

Foucault, Pagano, and Röell describe a mechanism as the market’s rules of the game. At minimum, those rules determine:

Permitted actions: which orders and cancellations participants may submit.
Observable state: which quotes, orders, identities, and trades participants can see.
Matching protocol: which compatible orders trade, at what price, and in what sequence.
Trading frequency: whether orders meet continuously or at scheduled calls.
Intermediation: whether customers meet directly or trade through dealers.

These choices affect more than implementation. They affect execution probability, waiting time, trading costs, information leakage, dealer inventory, and the distribution of surplus. [Foucault, Pagano, and Röell, introduction and ch. 1]

Four ways to organize the same trading interest

The interactive model deliberately holds participants constant. Only the mechanism changes.

Bilateral search

Buyers and sellers locate and negotiate with one another. Terms can reflect the particular pair, but finding and comparing counterparties consumes time. Trading interest is dispersed, so a participant cannot automatically know whether a better price exists elsewhere.

This structure is useful when trades require customization or relationship-specific judgment. It is weak when fast, repeated comparison is important.

Dealer market

A dealer posts prices at which the dealer will buy and sell. Customers gain immediacy: they can trade against the dealer instead of waiting for another customer. The dealer earns a spread but assumes inventory and information risk.

The dealer is not a magical source of liquidity. The dealer uses capital, manages inventory, updates quotes, and may later trade with another customer or dealer. If that service becomes risky or costly, quoted size can fall and the spread can widen.

Call auction

Orders accumulate and are matched together at a scheduled time, normally at one clearing price. Concentrating interest can increase the chance of finding the other side and reduce the influence of a momentary arrival imbalance. The cost is delay: a participant cannot necessarily trade immediately.

Calls are therefore natural when trading interest is sparse or when a market wants to concentrate liquidity at an open, close, or reopening.

Continuous limit order book

Participants submit priced orders to a shared book. A compatible incoming order executes against resting interest; otherwise it waits. Price priority usually ranks better prices first, with a secondary rule such as time priority for equal prices.

Continuous trading offers immediacy when compatible orders are already present. It also makes arrival order consequential. A patient trader may earn a better price by supplying a limit order, but assumes non-execution and adverse-selection risk.

Mechanism	Counterparty discovery	Price formation	Main service	Main cost or risk
Bilateral search	Trader searches	Pairwise negotiation	Custom terms	Search, delay, weak comparison
Dealer	Dealer stands between customers	Dealer bid and ask	Immediacy	Spread, inventory risk, information risk
Call auction	Venue pools orders	One clearing price	Concentrated liquidity	Must wait for the call
Continuous book	Venue matches incoming and resting orders	Sequence of book executions	Continuous access	Timing, queue, non-execution, leakage

No row is universally best. The appropriate design depends on the instrument, participation, urgency, trade size, information environment, and objectives of the market.

Liquidity is a service, not a synonym for volume

In this book, market liquidity means the ability to trade promptly, in useful size, without a large price concession relative to the market’s prevailing assessment of value.

That definition has several dimensions:

Tightness: how far execution prices are from a useful reference price.
Depth: how much can trade before prices move substantially.
Immediacy: how quickly a desired trade can be completed.
Resilience: how quickly liquidity and prices recover after an imbalance.

The quoted bid–ask spread measures one part of tightness. It does not, by itself, describe the cost of a large order, the likelihood of execution, or recovery after a shock. A market can show a narrow top-of-book spread and still be shallow or fragile.

Liquidity matters because transaction costs can prevent otherwise beneficial exchanges. It also matters before anyone trades: the option to sell later can make an asset more useful to hold today. Harris emphasizes that liquid exchange and hedging markets can improve specialization, risk sharing, and capital allocation. [Harris, ch. 9]

Price discovery is the other central service

Participants do not arrive with identical information. Some orders respond to public news, some reflect private analysis, and others arise from funding needs or risk reduction. A market combines these actions into observable quotes and transaction prices.

Price discovery is the process by which prices incorporate available information. It is not an instantaneous revelation of a known, objective number. The relevant value is uncertain, participants disagree, and order flow mixes information with non-informational demand.

Liquidity and price discovery can reinforce one another: low trading costs encourage participation and information production. They can also conflict. When liquidity suppliers suspect that incoming orders contain superior information, they may protect themselves by widening prices, reducing size, or withdrawing.

This tension explains why market quality cannot be reduced to “more trading” or “a smaller spread.”

What makes a market good?

A market design is only “good” relative to stated objectives. Possible objectives include:

Enabling useful trades at low total cost.
Producing prices that incorporate information accurately and promptly.
Supporting meaningful size without excessive price impact.
Remaining reliable during imbalances and operational stress.
Applying rules predictably and limiting avoidable advantages.
Making risks and responsibilities clear enough for participants to act.

These objectives can conflict. More transparency can aid comparison while exposing intentions. Continuous matching can provide immediacy while rewarding speed. Dealer commitment can provide execution while requiring compensation for risk. Batch trading can reduce the value of tiny timing advantages while making everyone wait.

Good analysis therefore separates:

Positive questions: What behavior and outcomes will this rule produce?
Normative questions: Which outcomes should the market prioritize?

Changing a matching rule is not merely a technical refactor. It changes economic incentives and redistributes costs, risks, and opportunities.

What the model leaves out

The visualization is a teaching model, not a market simulator. Its reservation values are fixed, participants submit one unit, all trades settle, and nobody behaves strategically. Real markets add:

Multiple price levels and quantities.
Arrival, cancellation, and communication latency.
Hidden or conditional orders.
Fees, rebates, tick sizes, and minimum quantities.
Inventory, funding, margin, and position limits.
Private information and strategic order placement.
Multiple venues and routing.
Clearing, settlement, and counterparty risk.
Outages, halts, and exceptional market states.

Later chapters add these complications one at a time. Keeping the first model small makes it possible to see exactly which conclusion changes when an assumption changes.

What you should internalize

People trade because assets, cash flows, and risks have different values to different participants.
A positive gain from trade can exist before any market mechanism is chosen.
Markets reduce the cost of discovering counterparties, comparing terms, coordinating time, and completing exchange.
A trading mechanism defines permitted actions, visible information, matching, pricing, and timing.
Dealers sell immediacy while assuming inventory and information risk.
Call auctions concentrate interest; continuous books make arrival sequence and queue position matter.
Liquidity is multidimensional. A spread is useful but incomplete.
Price discovery emerges from heterogeneous order flow; it can both support and threaten liquidity.
There is no universally best market structure. Evaluate a design against explicit objectives and constraints.

Retrieval drill

Using the six values in the visualization:

Identify every buyer–seller pair with a positive gain from trade.
Choose one pair and show how three different transaction prices divide the same total surplus.
Explain why a dealer’s bid and ask are not pure profit.
Explain one reason a call auction may outperform continuous trading for a thin instrument.
Name one market-quality improvement that could make another objective worse.

Sources

Larry Harris, Trading and Exchanges: Market Microstructure for Practitioners, Oxford University Press, 2002, chapters 8–9.
Thierry Foucault, Marco Pagano, and Ailsa Röell, Market Liquidity: Theory, Evidence, and Policy, first edition, Oxford University Press, 2013, introduction and chapter 1.

An Order Book Is a State Machine

A matching engine consumes an ordered command stream and produces a deterministic sequence of state changes and trades.

Part Market MechanicsModel Price-time priorityGoal Make every transition explainable

The visualization processes one input at a time. Notice that an incoming order is not automatically inserted into the book. It first trades against compatible resting orders. Only an unfilled remainder becomes resting state.

That leads to the chapter’s central model:

previous state + one valid input
    → next state + ordered outputs

If the same initial state and the same ordered inputs can produce different results, the matching engine is not deterministic.

The book is state, not a picture

A displayed order book is usually drawn as bids on one side and asks on the other. That picture is only a projection of deeper state:

Live orders and their remaining quantities.
Price levels and their aggregate quantities.
Queue order within each price level.
Stable order identities.
The sequence in which commands became authoritative.
Instrument state such as open, halted, or auctioning.

For a basic continuous limit order book:

Bids are ranked from highest price to lowest.
Asks are ranked from lowest price to highest.
The highest bid is the best bid.
The lowest ask is the best ask.
At one price, an earlier accepted order precedes a later order under time priority.

These are not merely display conventions. They determine who trades.

Commands and events are different

A participant sends a command:

Add order B1: buy 5 at 100
Cancel order B1
Replace order B1

The venue decides whether that command is valid, applies it to canonical state, and emits events:

Order accepted
Trade: 5 at 100
Order partially filled
Order rested
Order canceled
Command rejected

Keeping commands separate from events prevents a common systems mistake: treating a client’s intention as though it were already authoritative venue state.

An add command might produce:

A rejection and no state change.
One trade and no resting order.
Several trades across price levels.
Several trades followed by a resting residual.
No trade and one new resting order.

The input is singular. The output can be a sequence.

The smallest useful state

A clear reference model can use standard structures:

#![allow(unused)]
fn main() {
use std::cmp::Reverse;
use std::collections::{BTreeMap, HashMap, VecDeque};

type Price = i64;     // integer ticks, never floating point
type Quantity = u64;
type OrderId = u64;

struct Order {
    id: OrderId,
    price: Price,
    remaining: Quantity,
    accepted_sequence: u64,
}

struct Book {
    bids: BTreeMap<Reverse<Price>, VecDeque<OrderId>>,
    asks: BTreeMap<Price, VecDeque<OrderId>>,
    orders: HashMap<OrderId, Order>,
}
}

This representation makes the semantics visible:

The tree orders price levels.
The deque expresses FIFO priority at one price.
The hash map resolves an identity to live order state.
Prices use integer ticks, avoiding ambiguous floating-point equality.

It is a good specification model. It is not automatically the fastest production representation.

Processing an add

Consider an incoming buy limit order with limit price P and remaining quantity Q.

It can trade while both conditions hold:

Q > 0
best ask exists
best ask price <= P

At each step:

Select the best ask.
Select the first order at that price.
Execute the smaller of taker remaining quantity and maker remaining quantity.
Decrement both quantities.
Remove a fully filled maker.
Remove an empty price level.
Continue until the taker is filled or no compatible ask remains.
If quantity remains, append the residual to its bid-price queue.

The sell path is symmetric.

incoming buy crosses when limit >= best ask
incoming sell crosses when limit <= best bid

In the model above, each trade occurs at the resting order’s price. That is a common continuous-book convention, but an actual venue’s rulebook is authoritative.

Price priority before time priority

Suppose the ask book contains:

101: S1(4), S2(3)
102: S3(8)

An incoming buy for five units with a limit of 102:

Trades four with S1 at 101.
Trades one with S2 at 101.
Never reaches S3.

Price priority selects the 101 level before 102. Time priority selects S1 before S2.

The taker’s limit is a constraint, not a request to pay exactly that price.

Partial fills create residual state

If a buy for ten units finds only six compatible units, two things happen:

executed quantity = 6
remaining quantity = 4

If its order instructions allow the residual to rest, four units join the bid queue at the order’s limit price. If the instruction is immediate-or-cancel, those four units are canceled instead. The matching algorithm therefore cannot be separated completely from order instructions.

A production event stream must make the distinction explicit. “Order accepted” does not imply “order fully executed,” and “trade occurred” does not imply “order is terminal.”

Canceling by identity is the first representation trap

The hash map can find order B2 in expected constant time. That does not mean the order can be removed from the middle of a VecDeque in constant time.

HashMap lookup                 expected O(1)
find/remove inside VecDeque    O(n) in that price-level queue

A strict constant-time cancel path needs a stronger representation, such as:

Stable nodes in a slab or arena.
Intrusive previous/next links within each price queue.
A map from order ID to stable node handle.
Lazy tombstones with bounded cleanup.

This is the same structural issue encountered in strict LRU caches. A lookup table provides identity resolution; it does not automatically provide constant-time structural mutation.

The reference model should stay simple until profiling shows that cancel behavior matters. The optimized model must preserve exactly the same externally visible transitions.

Core invariants

An implementation should check invariants after every command in tests and debug builds.

Ordered price levels

bids: strictly descending price
asks: strictly ascending price

Positive live quantities

Every order stored in a price queue has remaining quantity greater than zero. Empty price levels do not exist.

No crossed resting book

After one command has been completely processed:

best_bid < best_ask

If the two sides are compatible, matching work remains. A locked or crossed book may appear in feeds for venue-specific reasons, but it should not appear accidentally in this simple matching model.

FIFO within one price

The accepted sequence numbers in a price queue are increasing. Canceling an order does not change the relative order of its surviving neighbors.

Index agreement

Every live order is reachable through both:

Its order-ID index.
Exactly one side and price queue.

No queue entry points to a missing order, and no indexed order is absent from the book.

Quantity conservation

For every accepted order:

original quantity
    = executed quantity
    + canceled quantity
    + live remaining quantity

This equation is useful in unit tests, replay validation, and production reconciliation.

Deterministic replay

A deterministic matcher is naturally event-sourced:

snapshot + commands after snapshot → current state

Replay supports:

Recovery after process failure.
Reproducing disputed executions.
Comparing two implementations.
Testing optimized code against a reference model.
Building historical books from authoritative events.

The ordering input must itself be authoritative. Wall-clock timestamps alone are insufficient when two messages can share a timestamp or arrive through different paths. A venue normally needs a total sequence, a single serialization point, or rules that produce an equivalent ordering.

For each processed command, record enough information to reproduce:

The command and participant identity.
Its authoritative sequence.
Validation outcome.
Generated trades in order.
Resting or terminal outcome.

Why the matching core is usually a single writer

The critical state is small but tightly coupled. Matching one command can touch:

The best price level.
Several maker orders.
Aggregate quantity.
The ID index.
The trade sequence.
The incoming order’s residual.

Allowing several threads to mutate these structures concurrently makes ordering and recovery much harder. A common architecture therefore uses one logical writer per partition:

network receive
    → parsing and validation
    → sequenced command queue
    → single matching-state owner
    → execution and market-data outputs

“Single writer” does not mean “the whole venue uses one CPU.” Instruments can be partitioned, and parsing, persistence, risk, and publication can run elsewhere. The design constraint is that one canonical order stream has one unambiguous mutation order.

This is an architectural starting point, not a universal law. Measure before adding coordination to the matching path.

Correctness before representation

Two implementations can expose the same state machine:

Concern	Clear reference	Possible optimized form
Price levels	`BTreeMap`	Flat ladder, radix structure, custom tree
FIFO at price	`VecDeque<OrderId>`	Intrusive queue over slab nodes
Identity	`HashMap<OrderId, Order>`	Dense handle table or specialized hash table
Allocation	Ordinary owned values	Preallocated arena or object pool
Outputs	Growable vector	Bounded ring or preallocated batch

Do not optimize by silently changing semantics. The fast implementation should be tested against the reference implementation using generated command streams.

The companion systems chapters explain the machinery:

This book owns the market semantics. The systems book owns representation, CPU behavior, networking, and measurement.

Failure cases worth testing

A useful test suite includes:

Duplicate order ID.
Unknown cancel.
Zero or overflowing quantity.
Invalid tick price.
Add that walks several levels.
Partial maker and partial taker fills.
Cancel of the head, middle, and tail of a queue.
Disconnect after the command becomes authoritative but before acknowledgment.
Replay containing a duplicate or missing sequence.
Snapshot taken between output publication steps.
Instrument halt while commands are queued.

Tests should assert the final book and the exact ordered output events.

What you should internalize

The book is canonical state; its visual ladder is only a projection.
Commands express intent. Events describe authoritative outcomes.
An incoming order matches before any residual rests.
Price priority chooses the level; time priority chooses within the level.
Partial execution changes quantity without necessarily terminating an order.
Fast identity lookup does not guarantee fast removal from a FIFO queue.
Invariants turn matching rules into executable correctness conditions.
Deterministic replay requires an authoritative total input order.
A single logical writer makes mutation order and recovery easier to reason about.
Optimize the representation only after preserving the reference state machine.

Retrieval drill

Using the event sequence in the visualization:

Why does S2 trade with B1 before B2?
Why does two units of B2 remain after S2 finishes?
At what price does B3 trade with S1, and why?
Which invariant would detect a zero-quantity order left in a queue?
What additional structure would make cancellation from a long price queue constant time?

Sources

Larry Harris, Trading and Exchanges: Market Microstructure for Practitioners, Oxford University Press, 2002, chapters 4 and 6.
Thierry Foucault, Marco Pagano, and Ailsa Röell, Market Liquidity: Theory, Evidence, and Policy, first edition, Oxford University Press, 2013, chapter 1.

Exact order types, amendment rules, precedence, and execution prices are venue-specific. Later venue chapters will use current rulebooks and protocol specifications as primary sources.

Orders and Execution Instructions

Status Draft briefPart Market Mechanics

An order is a conditional instruction, not simply an intention to buy or sell. Price, quantity, duration, visibility, routing, and contingency determine when it may execute.

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Electronic Markets from First Principles