Understand order book dynamics — Hinglish notes

6.3.1 · Stock-Market › Market Microstructure

Order Book KYA hota hai?

Sort order KYO hota hai? Exchange ko hamesha incoming party ke liye best available price pe trade karna hota hai. Isliye algorithm ko sirf har queue ke top ko dekhna padta hai — highest bid aur lowest ask. Sorting se $O (1)$ peek guarantee hoti hai "best" prices pe.

Order book ke saath ek order KAISE interact karta hai

Do fundamental order types hain, aur in dono ka difference samajhna microstructure ka 80% hai:

Size $Q$ ka ek market buy KAISE execute hota hai ("the walk"): Ye ask side ko upar se neeche eat karta hai. Pehle best ask ke against fill hota hai; agar us level ki depth khatam ho jaye, toh next-higher ask price pe move karta hai, aur aise tab tak chalta hai jab tak $Q$ fill na ho jaye. Isliye bade orders ko worse average prices milti hain — wo "book mein walk up" karte hain. Note: har partial match sirf matched quantity ko ek resting order se remove karta hai; us level ki baaki depth wahan rahi rehti hai.

Formula Book walk karne ka execution cost (derivation)

Maano ask side mein levels $(p_{1}, q_{1}), (p_{2}, q_{2}), \dots$ hain jisme $p_{1} < p_{2} < \dots$ (price ascending) aur depths $q_{i}$ hain. Size $Q$ ka ek market buy greedily fill karta hai.

Step 1 — dhundo kitne levels $k$ consume hote hain. $k$ wo sabse chhota integer hai jiske saath $\sum_{i = 1}^{k} q_{i} \geq Q$ ho. Kyun? Har level poori tarah eat hoti hai upar jaane se pehle, isliye hum depth tab tak accumulate karte hain jab tak wo $Q$ cover na kar le.

Step 2 — har level se kitni quantity li jaati hai. Levels $1.. k - 1$ se $q_{i}$ lo, aur level $k$ se remainder $r = Q - \sum_{i = 1}^{k - 1} q_{i}$ lo. Kyun? Aap last level se zyada kabhi nahi lete jitna zaroori ho — level $k$ ka baaki resting rehta hai.

Step 3 — total cash paid: $C = \sum_{i = 1}^{k - 1} p_{i} q_{i} + p_{k} r$ Kyun? Cost = price × quantity, har touched level pe summed.

Step 4 — average execution price aur slippage: $\overset{p}{ˉ} = \frac{C}{Q}, slippage = \overset{p}{ˉ} - a$ Kyun? Aap best ask $a = p_{1}$ pay karne ki umeed karte the; gap $\overset{p}{ˉ} - a$ impatience/size ki cost hai.

Spread aur imbalance KYO matter karta hai

OBI direction KYO predict karta hai: Agar $V_{b} ≫ V_{a}$ , toh bahut saare buyers wait kar rahe hain lekin sellers kam hain — ek chhota sa market sell price ko zyada push nahi kar sakta, jabki ek market buy easily ask lift kar deta hai. Price upar drift karne lagti hai. OBI $\to + 1$ = buy pressure; OBI $\to - 1$ = sell pressure. Ye ek weak, fleeting predictor hai kyunki book har millisecond mein badlti hai.

Worked Examples

Worked example Example 1 — Book padho aur spread/mid compute karo

Book snapshot:

Bid Qty	Bid Px	Ask Px	Ask Qty
300	100.00	100.05	200
500	99.99	100.06	400

Best bid $b = 100.00$ . Kyun? Highest buy price top pe hoti hai.
Best ask $a = 100.05$ . Kyun? Lowest sell price top pe hoti hai.
Spread $s = 100.05 - 100.00 = \$ 0.05$.
Mid $m = (100.05+100.00)/2 = \$ 100.025$.

Common Mistakes (Steel-man + fix)

Active Recall

Recall Quick self-test (pehle answers chhupao, forecast karo)

Q: Bid side ke bilkul top pe kya hota hai? → Highest buy price (best bid).
Q: Spread aur mid ka formula? → $s = a - b$ , $m = (a + b) /2$ .
Q: Maker vs taker ek-ek word mein? → Maker liquidity add karta hai; taker remove karta hai.
Q: Bade market orders ko worse average prices kyun milti hain? → Wo multiple levels consume karte hue upar/neeche walk karte hain.
Q: Jab do orders match karte hain, exactly kya remove hota hai? → Sirf matched quantity; koi bhi remainder resting rehta hai.
Q: OBI $= + 0.8$ ka matlab? → Strong buy-side pressure, short-term upward drift likely.

Recall Feynman: ek 12-saal ke bachche ko explain karo

Socho ek lemonade stand market. Ek wall pe bacche likhte hain "Main ek cup ke liye $2 d u n g a! " (hi g h es tp r i ce t o pp e) . D oosr i w a l l p ese l l er s l ik h t e hain " M ain$ 2.10 mein bechunga!" (lowest top pe). Dono ke beech ka chhota sa gap ($0.10) spread hai. Agar ek pyaasa bachcha kehta hai "abhi lemonade do kisi bhi price pe," toh wo pehle sabse saste seller ko pakadta hai, phir usse agle saste ko, har cup ke liye thoda zyada pay karta hua — yahi walking the book hai. Agar ek seller ke paas 10 cups the lekin bachche ko sirf 4 chahiye the, toh sirf 4 cups bikenge aur baaki 6 wall pe likhe rahe. Agar bahut zyada buyers wait kar rahe hain sellers se zyada, toh prices jaldi upar creep karenge. Book bas sabki notes hai ki wo kya karenge, aur ye badlti rehti hai jab bacche apni notes add ya erase karte hain.

Connections

Bid-Ask Spread — wo core cost jo book ke top level mein embedded hai.
Market Makers and Liquidity Provision — book kaun fill karta hai aur kyun.
Slippage and Market Impact — "walk" ko quantify karna.
Order Types (Limit, Market, Stop, Iceberg) — book ke ingredients.
High-Frequency Trading — millisecond book dynamics exploit karne wale agents.
Price Discovery — crossing orders "true" price kaise set karte hain.

Limit order book kya hota hai?

Ek continuously-updated, price-ranked record jo saare resting limit orders ka hota hai, bid side (highest price top pe) aur ask side (lowest price top pe) mein split.

Best bid aur best ask kya hote hain?

Best bid = highest price jo ek buyer pay karega; best ask = lowest price jo ek seller accept karega.

Spread aur mid price define karo.

Spread

s = a - b

; mid

m = (a + b) /2

, jahan

a

=best ask,

b

=best bid.

Maker vs taker?

Maker ek resting limit order post karta hai (liquidity add karta hai); taker ek marketable/market order bhejta hai jo spread cross karke liquidity remove karta hai.

Bade market orders ko slippage kyun hoti hai?

Wo best level exhaust karte hain phir progressively worse price levels ke against execute karte hain ("walking the book"), average execution price ko best quote se upar le jaate hain.

Jab do orders match karte hain, book se kaunsi quantity remove hoti hai?

Sirf matched (overlapping) quantity = dono sizes mein se min; bade order ka koi bhi unfilled remainder resting rehta hai.

Book walk karne par average execution price ka formula?

\overset{p}{ˉ} = C / Q

jahan

C = \sum_{i = 1}^{k - 1} p_{i} q_{i} + p_{k} r

r = Q - \sum_{i = 1}^{k - 1} q_{i}

Order-book imbalance define karo aur uske sign ka matlab batao.

OBI = (V_{b} - V_{a}) / (V_{b} + V_{a}) \in [- 1, 1]

; positive = buy pressure/upward drift, negative = sell pressure.

Market order se aap actually kis price pe trade karte ho?

Buyers ask pay karte hain, sellers bid receive karte hain — kabhi mid nahi.

Limit order kab rest karta hai vs immediately execute hota hai?

Ye immediately execute hota hai agar ye cross kare (buy price

\geq

best ask, ya sell price

\leq

best bid); warna book mein rest karta hai.

Displayed book cost ka sirf optimistic estimate kyun hota hai?

Hidden/iceberg orders hote hain aur doosre participants react karke cancel/add karte hain, isliye realized slippage usually book-implied slippage se zyada hoti hai.