Learn about limit order book depth — Stock-Market notes

WHAT is a Limit Order Book?

Definition Core terms

Limit order: an order to buy/sell a fixed quantity at a specified price or better. It rests in the book until matched (unlike a market order, which executes immediately at whatever price is available).
Bid side: all resting buy limit orders, sorted from highest price (best bid) downward.
Ask (offer) side: all resting sell limit orders, sorted from lowest price (best ask) upward.
Best bid $b_1$ / best ask $a_1$ : the top of each side — the current tradable prices.
Spread: $s = a_1 - b_1$ (always $\ge 0$ ; if it hit $0$ the orders would match).
Mid price: $m = \dfrac{a_1 + b_1}{2}$ .
Depth at a level: the total resting quantity $q_i$ at price $p_i$ .
Cumulative depth up to level $k$ : $Q_k = \sum_{i=1}^{k} q_i$ — total shares available if you sweep through the first $k$ levels.

HOW price moves: walking the book

When a market buy of size $V$ arrives, it eats the ask side from the top:

Derivation Effective execution price — from first principles

WHAT we want: the average price paid to buy $V$ shares against the ask ladder.

Setup. Ask levels are $(a_1,q_1),(a_2,q_2),\dots$ with $a_1<a_2<\dots$ A market buy fills the cheapest shares first (price–time priority).

Step 1 — how many levels get consumed? Find the smallest $k$ such that cumulative depth covers the order: $Q_{k-1} < V \le Q_k, \qquad Q_k=\sum_{i=1}^k q_i.$ Why this step? Because the order can't reach level $k+1$ until levels $1..k$ are exhausted — that's the price-time priority rule.

Step 2 — cost to fill. Fully consume levels $1..k-1$ , then take the remainder $V-Q_{k-1}$ from level $k$ : $\text{Cost} = \sum_{i=1}^{k-1} q_i\,a_i \;+\; (V - Q_{k-1})\,a_k.$ Why this step? Each share costs the price of the level it came from; we only partially fill the last level.

Step 3 — average (VWAP) execution price: $\boxed{\;\bar{p}(V) = \frac{\sum_{i=1}^{k-1} q_i a_i + (V-Q_{k-1})a_k}{V}\;}$

Step 4 — price impact / slippage relative to the mid: $\text{Impact}(V) = \bar{p}(V) - m.$ Why this step? Impact isolates the extra cost caused by finite depth. If the book were infinitely deep at $a_1$ , impact would just be half the spread.

Figure — Learn about limit order book depth

Worked Example 1 — Small order, one level

Worked Example 2 — Large order, walks two levels

Worked Example 3 — Same order, shallow book

Worked example Buy 700, but

$q_1=200$ instead of 500 Ladder: $(100.0,200),(100.1,300),(100.3,400)$ . Step 1: $Q_1=200$ , $Q_2=500<700\le Q_3=900 \Rightarrow k=3$ . Step 2: Cost $=200(100.0)+300(100.1)+(700-500)(100.3)=20000+30030+20060=70090$ . Step 3: $\bar p=70090/700=100.1286$ . Step 4: impact $=0.1786$ — more than double Example 2 for the same order size. Steel-man lesson: identical trade, identical top-of-book price, but thin depth ⇒ far worse fill. Depth, not just spread, controls your cost.

Common Mistakes

Flashcards

What is a limit order (vs a market order)?

A resting order to trade a fixed quantity at a specified price or better; it waits in the book. A market order executes immediately at the best available prices, consuming liquidity.

Define depth at a price level.

The total resting order quantity

q_i

available at that price.

Define cumulative depth

Q_k

Q_k=\sum_{i=1}^k q_i

— total volume from the best level through level

k

Formula for the spread and mid price?

s=a_1-b_1

;

m=(a_1+b_1)/2

How do you find how many ask levels a market buy of size

V

consumes?

The smallest

k

with

Q_{k-1}<V\le Q_k

Write the VWAP (average) execution price for buying

V

\bar p(V)=\dfrac{\sum_{i=1}^{k-1}q_i a_i+(V-Q_{k-1})a_k}{V}

Define slippage / price impact of a trade.

\bar p(V)-m

: the extra average cost above the mid caused by walking the finite-depth book.

Why can a tight-spread stock be expensive to trade in size?

If depth is thin, a large order walks into far worse levels, so slippage dwarfs the small spread.

What is order-book imbalance and what does it hint at?

I=\dfrac{Q^{bid}-Q^{ask}}{Q^{bid}+Q^{ask}}

; positive

I

(more bids) suggests short-term upward price pressure.

When walking the book, why weight the last level by

V-Q_{k-1}

Because the final level is only partially filled — only the remaining shares after exhausting earlier levels come from it.

Recall Feynman: explain to a 12-year-old

Imagine a candy shop where people line up notes saying "I'll SELL you candy for ₹10" or "I'll BUY your candy for ₹9". The sell notes are stacked cheapest-first, the buy notes highest-first. Depth is how many candies each note is good for. If you want to buy 100 candies but the cheapest note only covers 20, you have to grab the next note (a bit pricier), then the next… so buying a lot pushes the price up as you go. A shop with big fat notes (deep book) barely changes price; a shop with tiny notes (thin book) jumps a lot. That's the whole idea!

Connections

Bid-Ask Spread — the top-of-book cost; depth explains the cost beyond it.
Market Orders vs Limit Orders — who consumes vs supplies liquidity.
Price-Time Priority — the matching rule that dictates fill order.
Slippage and Market Impact — direct consequence of finite depth.
Order-Book Imbalance — depth asymmetry as a short-term price signal.
VWAP and TWAP Execution — algorithms that slice orders to avoid walking the book.
Liquidity — depth is one of its three pillars (tightness, depth, resiliency).

Concept Map

Hinglish (regional understanding)

Intuition Hinglish mein samjho

Socho ek shop mein do lines lagi hain — ek taraf log likh ke rakhte hain "main ₹9 mein KHAREEDunga" (ye hai bid side), aur doosri taraf "main ₹10 mein BECHunga" (ye hai ask side). In sab resting orders ka collection hi limit order book hai. Har price pe kitni quantity padi hai — usko bolte hain depth. Top ki best bid aur best ask ke beech ka gap = spread, aur unka average = mid price.

Ab asli baat: jab tum market buy maarte ho, tum sabse sasti ask se bharna shuru karte ho (price-time priority). Agar tumhara order chhota hai, ek hi level se ban jaata hai — sirf aadha spread ki cost. Lekin agar order bada hai aur upar wala level patla (thin depth) hai, to tumhe agle, mehenge levels tak "walk" karna padta hai. Isse tumhara average fill price (VWAP) mid se upar chala jaata hai — ye extra cost hi slippage / price impact hai. Formula: $\bar p(V)=\frac{\sum q_i a_i+(V-Q_{k-1})a_k}{V}$ .

Kyun important hai? Kyunki bahut log sochte hain "spread chhota hai to trade sasta hai" — galat! Agar depth kam hai to same order mein bahut zyada slippage lag sakta hai (dekho Example 2 vs Example 3 — same 700 shares, par thin book mein double impact). Isliye bade traders order ko chote tukdon mein todte hain (VWAP/TWAP algos) taaki book "walk" na ho.

Ek aur cheez — imbalance: agar bid side pe depth zyada hai ask se, to short-term mein price upar jaane ka pressure hota hai ( $I=\frac{Q^{bid}-Q^{ask}}{Q^{bid}+Q^{ask}}$ ). To depth sirf cost nahi, direction ka bhi hint deta hai. Yaad rakho: "Spread is the door, depth is the room."

Test yourself — Market Microstructure

Connections