Learn about limit order book depth — Hinglish notes

6.3.2 · Stock-Market › Market Microstructure

LOB KYA hai? (WHAT is a Limit Order Book?)

Definition Core terms

Limit order: ek order buy/sell karne ka ek fixed quantity ko specified price ya usse better price par. Yeh book mein rest karta hai jab tak match na ho (market order se alag, jo immediately available price par execute hota hai).
Bid side: saare resting buy limit orders, highest price (best bid) se neeche sort kiye hue.
Ask (offer) side: saare resting sell limit orders, lowest price (best ask) se upar sort kiye hue.
Best bid $b_{1}$ / best ask $a_{1}$ : har side ka top — current tradable prices.
Spread: $s = a_{1} - b_{1}$ (hamesha $\geq 0$ ; agar yeh $0$ ho jaaye toh orders match ho jaate).
Mid price: $m = \frac{a _{1} + b _{1}}{2}$ .
Depth at a level: price $p_{i}$ par total resting quantity $q_{i}$ .
Cumulative depth level $k$ tak: $Q_{k} = \sum_{i = 1}^{k} q_{i}$ — total shares available agar tum pehle $k$ levels sweep karo.

Price kaise move hoti hai: book ko walk karna

Jab ek market buy of size $V$ aata hai, toh yeh ask side ko top se khaata hai:

Derivation Effective execution price — first principles se

WHAT we want: $V$ shares kharidne ke liye ask ladder ke against average price paid.

Setup. Ask levels hain $(a_{1}, q_{1}), (a_{2}, q_{2}), \dots$ jisme $a_{1} < a_{2} < \dots$ Market buy sabse sasti shares pehle fill karta hai (price–time priority).

Step 1 — kitne levels consume hote hain? Sabse chhota $k$ dhundo jisme cumulative depth order cover kare: $Q_{k - 1} < V \leq Q_{k}, Q_{k} = \sum_{i = 1}^{k} q_{i} .$ Yeh step kyun? Kyunki order level $k + 1$ tak nahi pahunch sakta jab tak levels $1.. k$ exhaust na ho jaayein — yahi price-time priority rule hai.

Step 2 — fill karne ki cost. Levels $1.. k - 1$ fully consume karo, phir remainder $V - Q_{k - 1}$ level $k$ se lo: $Cost = \sum_{i = 1}^{k - 1} q_{i} a_{i} + (V - Q_{k - 1}) a_{k} .$ Yeh step kyun? Har share ki cost usi level ki price hoti hai jahan se woh aaya; hum last level ko sirf partially fill karte hain.

Step 3 — average (VWAP) execution price: $\overset{p}{ˉ} (V) = \frac{\sum _{i = 1}^{k - 1} q _{i} a _{i} + ( V - Q _{k - 1} ) a _{k}}{V}$

Step 4 — price impact / slippage mid ke relative: $Impact (V) = \overset{p}{ˉ} (V) - m .$ Yeh step kyun? Impact isolate karta hai finite depth ki wajah se extra cost. Agar book infinitely deep hoti $a_{1}$ par, toh impact sirf half spread hota.

Figure — Learn about limit order book depth

Worked Example 1 — Chhota order, ek level

Worked Example 2 — Bada order, do levels walk karta hai

Worked Example 3 — Same order, shallow book

Common Mistakes

Flashcards

Limit order kya hota hai (market order se compare mein)?

Ek resting order ek fixed quantity trade karne ka ek specified price ya better par; yeh book mein wait karta hai. Market order immediately best available prices par execute hota hai, liquidity consume karta hai.

Ek price level par depth define karo.

Us price par total resting order quantity

q_{i}

available.

Cumulative depth

Q_{k}

define karo.

Q_{k} = \sum_{i = 1}^{k} q_{i}

— best level se level

k

tak ka total volume.

Spread aur mid price ka formula?

s = a_{1} - b_{1}

;

m = (a_{1} + b_{1}) /2

Tum kaise pata karte ho ki size

V

ka market buy kitne ask levels consume karta hai?

Sabse chhota

k

jisme

Q_{k - 1} < V \leq Q_{k}

ho.

V

kharidne ka VWAP (average) execution price likho.

\overset{p}{ˉ} (V) = \frac{\sum _{i = 1}^{k - 1} q _{i} a _{i} + ( V - Q _{k - 1} ) a _{k}}{V}

Trade ka slippage / price impact define karo.

\overset{p}{ˉ} (V) - m

: mid se upar extra average cost jo finite-depth book ko walk karne se aati hai.

Kyun tight-spread stock size mein expensive trade karna ho sakta hai?

Agar depth thin hai, toh bada order bahut kharab levels mein walk kar jaata hai, isliye slippage chhote spread ko dwarf kar deta hai.

Order-book imbalance kya hai aur yeh kya hint karta hai?

I = \frac{Q ^{bi d} - Q ^{a s k}}{Q ^{bi d} + Q ^{a s k}}

; positive

I

(zyada bids) short-term upward price pressure suggest karta hai.

Book walk karte waqt, last level ko

V - Q_{k - 1}

se kyun weight karte hain?

Kyunki final level sirf partially fill hota hai — sirf remaining shares jo earlier levels exhaust karne ke baad bachte hain wahan se aate hain.

Recall Feynman: 12-saal ke bachche ko explain karo

Ek candy shop imagine karo jahan log notes laga ke jaate hain "Main tumhe ₹10 mein candy BECHUNGA" ya "Main tumhari candy ₹9 mein KHAREEDUNGA". Sell notes sabse saste-pehle stack hote hain, buy notes highest-pehle. Depth hai kitni candies ke liye har note valid hai. Agar tum 100 candies kharidna chahte ho lekin sabse sasta note sirf 20 cover karta hai, toh tumhe agla note pakadna hoga (thoda mehenga), phir agla… toh bahut saari candies kharidna price ko upar push karta hai jaate jaate. Bade fat notes wali dukaan (deep book) mein price muskil se badlti hai; tiny notes wali dukaan (thin book) mein bahut jump karta hai. Bas yahi poora idea hai!

Connections

Bid-Ask Spread — top-of-book cost; depth explain karta hai cost usse aage.
Market Orders vs Limit Orders — kaun liquidity consume karta hai vs supply karta hai.
Price-Time Priority — matching rule jo fill order dictate karta hai.
Slippage and Market Impact — finite depth ka direct consequence.
Order-Book Imbalance — depth asymmetry as a short-term price signal.
VWAP and TWAP Execution — algorithms jo orders slice karte hain book walk karne se bachne ke liye.
Liquidity — depth uske teen pillars mein se ek hai (tightness, depth, resiliency).