Understand price impact and market depth — Hinglish notes

6.3.3 · Stock-Market › Market Microstructure

WHAT are we talking about?

WHY does price impact exist? (first principles)

Bas itna hi — koi magic nahi. Impact woh price hai jo tum pay karte ho immediacy demand karne ke liye ek finite pool of liquidity se.

Figure — Understand price impact and market depth

HOW to derive price impact from the order book (walking the book)

Maano tum buy karna chahte ho $Q$ shares as a market order. Ask side mein levels hain:

$(p_{1}, q_{1}), (p_{2}, q_{2}), (p_{3}, q_{3}), \dots p_{1} < p_{2} < p_{3} < \dots$

jahaan $p_{1}$ best ask hai aur $q_{i}$ price $p_{i}$ pe quantity hai.

Step 1 — Greedily fill karo. Tum $q_{1}$ consume karte ho $p_{1}$ pe, phir $q_{2}$ $p_{2}$ pe, ... jab tak total $= Q$ na ho jaaye. Yeh step kyun? Matching engine hamesha tumhe best available price pe pehle fill karta hai — tum kisi saste seller ko skip nahi kar sakte.

Step 2 — Total cost. Agar levels $1.. k - 1$ fully fill ho jaayein aur tum level $k$ se $r$ lete ho:

$Cost = \sum_{i = 1}^{k - 1} p_{i} q_{i} + p_{k} r, r = Q - \sum_{i = 1}^{k - 1} q_{i}$

Yeh step kyun? Cost bas price × quantity hai jo har level pe sum ki gayi jise tum touch karte ho.

Step 3 — Average execution price (tumhare fills ka VWAP).

$\overset{p}{ˉ} = \frac{Cost}{Q}$

Step 4 — Price impact = pre-trade mid ke against slippage. Maano trade se pehle mid price $m_{0}$ ho:

$Impact = \overset{p}{ˉ} - m_{0}$

Yeh step kyun? Mid $m_{0}$ "fair" reference hai isse pehle ki tumne kuch disturb kiya; tumhara average fill usse kitna upar hai wahi tumhara impact ka cost hai (a.k.a. slippage).

Empirical "square-root law" (derivation sketch)

Traders observe karte hain ki size $Q$ ke metaorder ka impact linearly se kam badhta hai — roughly:

$Δ p \approx Y σ \frac{Q}{V}$

jahaan $σ$ = daily volatility, $V$ = daily volume, $Y$ = constant $\sim 0.5$ – $1$ .

Worked Examples

Common Mistakes (Steel-manned)

Flashcards

Market depth kya hai?

Best prices pe trade karne ke liye available cumulative quantity, jab tak price given amount move na kare; deep = bada volume thodi movement ke saath absorb ho sakta hai.

Price impact kya hai?

Tumhare apne trade se hone wala price change — average fill price minus pre-trade mid price (slippage).

Temporary aur permanent impact mein kya fark hai?

Temporary order khatam hone ke baad revert hota hai (liquidity consume hoti hai phir refill hoti hai); permanent rehta hai kyunki trade ne information reveal ki jo fair value update karti hai.

Buying price ko upar kyun push karti hai (do mechanisms)?

(1) Mechanical: tum saste sellers consume karte ho aur mehnge waalon tak pahunchte ho; (2) Informational: market makers bada buyer dekhkar quotes raise karte hain.

Book walk karte waqt average execution price ka formula?

\overset{p}{ˉ} = Cost / Q

jahaan Cost

= \sum p_{i} q_{i}

consumed levels mein.

Impact ka square-root law batao.

Δ p \approx Y σ Q / V

, jahaan

σ

volatility,

V

daily volume,

Y \sim 0.5

–1.

Impact concave (square-root) kyun hai, linear kyun nahi?

Price move hone pe latent/limit liquidity replenish hoti hai, isliye har additional share kam hurt karta hai — book elastic hai.

Kya bid-ask spread aur price impact same hain?

Nahi — spread tiny round trip ka fixed cost hai; impact order size ke saath top of book se aage badhta hai.

Price P tak depth ka formula?

D (P) = \sum_{p_{i} \leq P} q_{i}

— total quantity jo P pe ya usse neeche sell ki ja sakti hai.

Book (100.0,200),(100.1,300) ke saath 400 buy karo; avg price kya hoga?

(200 \cdot 100.0 + 200 \cdot 100.1) /400 = 100.05

Recall Feynman: 12-saal ke bachche ko samjhao

Socho ek candy shop hai jahaan saste candies saamne hain aur mehngi waalon peeche. Agar tum sirf ek candy kharееdo, tum sasta front price pay karte ho. Lekin agar tum saari candies khareedna chahte ho, tum sasti waalon khatam kar lete ho aur peeche ki mehngi waalon ke liye pay karna shuru ho jaata hai — toh tumhara average price badhta jaata hai sirf isliye kyunki tumne bahut zyada khareedа. "Price impact" woh extra hai jo tum ek saath bahut zyada khareedne ke liye pay karte ho. "Market depth" yeh hai ki saamne kitni sasti candies rakhi hain: ek shop jo bahut bhari ho (deep) barely price change karti hai; ek shop mein 2 candies (thin) price instantly jump kar jaata hai.

Connections

Limit Order Book — woh structure jisse impact derive kiya jaata hai
Bid-Ask Spread — level-1 cost jisse impact aage jaata hai
Liquidity — depth liquidity ka ek dimension hai (tightness aur resiliency ke saath)
Slippage — expected price se realized deviation
VWAP and TWAP Execution — algorithms jo orders split karte hain impact reduce karne ke liye
Market Makers — jo depth provide karte hain aur information pe reprice karte hain
Volatility — square-root law mein $σ$ scaling factor
Order Types — market vs limit orders aur yeh kaise liquidity demand/supply karte hain