2.1.1 Market Microstructure from Zero

Basic Prerequisites: Market Microstructure & Order Types - Hub (or none - this page needs no prior finance).

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1. Intuition & Practical Objective

This page builds the why of market microstructure with no prior trading knowledge. The goal is one idea: a market is a mechanism that prices immediacy, and every order you send is a request to buy or sell that immediacy at a rate set by whoever is willing to wait.

Start with the dumbest question: who is on the other side of my trade? Somebody, somewhere, is holding the opposite position. In a modern electronic market that someone is a matching engine: a deterministic program that pairs buy and sell instructions by published rules - first by price (best price first), then by time (first-in-first-out among equal prices). Nobody negotiates; the rules are the contract.

Three “aha”s take you from “I click buy” to a working mental model:

1. There are two kinds of traders in every fill. The maker posts a resting order and supplies liquidity (they wait); the taker sends an order that crosses the spread and consumes it (they act now). The maker earns the spread as compensation for waiting and for the risk of being wrong; the taker pays it as the price of certainty. The bid-ask spread is the price of immediacy.

2. “The price” is really several prices at once. At one instant there is a best bid, a best ask, a mid, a micro-price (size-weighted), a last-trade price, and hypothetical prices for buying more size. Hasbrouck (Ch 1) stresses this: prices are multiple and mechanism-dependent. Microstructure is the study of those gaps.

3. Waiting is not free - it is a loan you make to strangers. A resting limit order is an option written for free to everyone else: they may fill you exactly when your price has become bad (you get adversely selected) and leave you alone when it has become good. That asymmetry - not commission - is the true cost of liquidity provision.

The landscape in one picture. Orders are typed instructions; venues are mechanisms that accept them: exchanges (continuous limit-order markets, sometimes with call auctions at the open/close), dark pools (no displayed quotes, often midpoint matching), and OTC / dealer markets (a dealer quotes a two-sided price and you trade against their balance sheet). Every later Pillar 2 topic - execution algorithms, optimal execution, fill probability, low-latency systems - is downstream of the vocabulary on this page.

The one-sentence essence. “Microstructure is the economics of immediacy: makers wait and are paid the spread while bearing adverse selection, takers cross and pay it, and the matching engine decides who is first.”

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2. Mathematical Ground Truth & Derivations

The Roll model: decomposing a trade price (Hasbrouck Ch 3). The simplest formal statement of the idea that the spread is a waiting cost. Let the efficient (latent consensus) price follow a random walk, $m_t=m_{t-1}+u_t$ with $\mathrm{Var}(u_t)={\sigma }_u^2$, and let a dealer/liquidity supplier charge a half-spread $c$ around it. The observed trade price is

$$p_t=m_t+q_{t}c,q_t=\{\begin{array}{ll}+1& \text{buy}\\ -1& \text{sell}\end{array},$$

with buys/sells equally likely and serially independent of $u_t$. Define price changes $\Delta p_t=p_t-p_{t-1}$. Then

$$\Delta p_t=c(q_t-q_{t-1})+u_t.$$

Taking moments (and using $\mathrm{Var}(q_t)=1$, $\mathrm{Cov}(q_t,q_{t-1})=0$):

$$\boxed{{\gamma }_0\equiv \mathrm{Var}(\Delta p_t)=2c^2+{\sigma }_u^2,{\gamma }_1\equiv \mathrm{Cov}(\Delta p_{t-1},\Delta p_t)=-c^2}$$

and all higher autocovariances vanish. This is the entire content of the Roll model: the bid-ask bounce ($c^2$) creates a negative first-order autocorrelation in trade-price changes, while the efficient-price innovation contributes only contemporaneous variance. Inverting:

$$\boxed{c=\sqrt{-{\gamma }_1},{\sigma }_u^2={\gamma }_0+2{\gamma }_1,\text{quoted spread}=2c=2\sqrt{-{\gamma }_1}.}$$

Why this matters. The spread $2c$ is estimable from trade prices alone - a pure microstructure signal hidden inside an otherwise near-random-walk price series. Empirically (Hasbrouck Ch 3, PCO Oct 2003) ${\hat{\gamma }}_1=-0.0000294$ gives $c=$ $0.017, spread $0.034, close to the observed time-weighted NYSE average of $0.032 - a striking confirmation.

The same spread, from information (Foucault Ch 1; Hasbrouck Ch 5). The Roll $c$ is a cost of waiting; the Glosten–Milgrom spread is a cost of being picked off. With informed arrival proportion $\mu$ and value dispersion $(V_H-V_L)$, the symmetric-prior spread is $A-B=(V_H-V_L)\mu$ - the model-free intuition that more adverse selection widens the spread. Both costs coexist: the quoted spread pays for order processing, inventory, and adverse selection at once.

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3. Computational Implementation - recovering the spread from trade prices

Simulate the Roll data-generating process and recover $c$ from the autocovariances, exactly as an econometrician would from tape data. Standard library only; re-executed and reproduced.

Read the numbers. The near-exact recovery $\hat{c}=0.0195$ versus the true $c=0.02$ (and ${\hat{\gamma }}_1=-0.00038$ versus theory $-0.00040$) shows the bounce signal survives in a price series whose innovations are five times larger (${\sigma }_u=0.10$) than the spread component - the spread is small but systematic, so autocovariance exposes it. The last two lines are the whole economics of liquidity: taking costs $2$ bps, making earns $2$ bps but only when the order fills - and the orders that fill are disproportionately the ones you did not want to fill.

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4. Failure Modes & First-Principles Breakdowns

1. Confusing “the price” with the executed price. The last trade, the mid, and the price you will actually get are three different numbers. The beginner error is to model execution at the mid; you cross the spread as a taker and forgo it as a maker.
2. Treating the spread as a fee. The half-spread $c$ is not a constant toll - it widens with adverse selection, volatility, and inventory stress (Foucault Ch 3). Quoting a fixed spread through a news event is a guaranteed loss to informed flow.
3. Ignoring adverse selection when providing liquidity. Passive orders earn the spread on average across all fills, but the fills are not a random sample: they cluster in the states where the price is about to move against you. A resting order is a short option; see 05 · Failure Modes.

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5. References

• Hasbrouck, Joel - Empirical Market Microstructure (2007)
• Foucault, Pagano & Röell - Market Liquidity (2013)
• Harris, Larry - Trading and Exchanges (2003). *The accessible map of traders, orders, and venues
• O’Hara, Maureen - Market Microstructure Theory (1995). The model-based foundation beneath the Roll and Glosten–Milgrom ideas.

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6. Connected Graph Bridges

• Continue: 02 · Order Types · Index Hub
• Book mechanics: Limit Order Book Mechanics
• The spread, decomposed: Spread Decomposition & the Roll Model · Adverse Selection & Glosten–Milgrom
• Base: Probability & Measure Theory