Understand auction mechanisms — Hinglish notes

6.3.7 · Stock-Market › Market Microstructure

Auction mechanism KYA hota hai?

Exchanges call auctions kyun use karte hain?

Un moments par liquidity aggregate karne ke liye jab woh patli ya uncertain ho (market open, market close, halt ke baad).
Kaafi saari jittery prices ki jagah ek fair, single reference price dhundhne ke liye.
"Pehle hone" ka fayda kam karne ke liye — batch mein sabko ek hi price milti hai.

Call auction price kaise dhundhta hai — scratch se derive karo

Hum woh price $p$ chaahte hain jo trade ho sakne waale shares ki sankhya maximise kare. Aao dono functions pehle principles se banate hain.

Step 1 — Cumulative quantities define karo. Maano $B (p)$ total buy quantity hai jo price $p$ par trade karne ko taiyaar hai, aur $S (p)$ total sell quantity.

$B (p) = \sum_{i : limit_{i} \geq p} q_{i}^{buy}, S (p) = \sum_{j : limit_{j} \leq p} q_{j}^{sell}$

Yeh step kyun? Kyunki limit ek worst acceptable price hai, exact price nahi — buyers koi bhi lower price accept karte hain, sellers koi bhi higher price.

Step 2 — Price $p$ par Executable volume. Tum sirf do sides mein se chhoti side trade kar sakte ho (unmatched share ke saath koi trade nahi hoti):

$V (p) = min (B (p), S (p))$

Min kyun? Agar 500 khareedna chahte hain lekin sirf 300 bechna chahte hain, toh sirf 300 trades hoti hain — extra 200 buyers unfilled rah jaate hain.

Step 3 — Auction price. Woh price chuno jo executable volume maximise kare:

$p^{*} = ar g p max V (p) = ar g p max min (B (p), S (p))$

Max kyun? Exchange ka stated objective maximum executable volume hai — yaani zyada se zyada shares haath badlein.

Step 4 — Tie-breaking rules (WHY they exist). $B$ ek non-increasing step function hai aur $S$ non-decreasing hai, isliye $min (B, S)$ aksar prices ki ek range par flat hoti hai. Exchanges ties ko is order mein break karte hain:

Max volume (yeh ho chuka).
Minimum imbalance — woh $p$ chuno jo $∣ B (p) - S (p) ∣$ minimise kare (kam se kam leftover).
Market pressure — agar imbalance ka sign fixed hai, toh pressured side ke kareeb wali price chuno.
Reference price — last / previous close ke sabse kareeb.

Worked Example 1 — full order book crossing

Worked example Clearing price dhundho

Buy orders: 100@$50, 200@$49, 300@$48. Sell orders: 150@$47, 200@$48, 250@$49.

$B (p)$ banao (buyers $\leq$ apni limit par accept karte hain, yaani limit $\geq p$ ):

$p$	kaun qualify karta hai	$B (p)$
47	saare buyers (limits ≥47)	600
48	$48+$49+$50	600
49	$49+$50	300
50	sirf $50	100

Kyun? $50 waala buyer $47 par khushi se trade karega; $48 waala buyer $49 par trade NAHI karega.

$S (p)$ banao (sellers jinki limit $\leq p$ hai):

$p$	qualify karta hai	$S (p)$
47	sirf $47	150
48	$47+$48	350
49	$47+$48+$49	600

$V = min (B, S)$ compute karo:

$p$	$B$	$S$	$V$
47	600	150	150
48	600	350	350
49	300	600	300

Max volume hai 350 at $48 → ** $p^*=\$ 48 $, 350 shares trade hote hain.** *Yeh step kyun?* \$ 48 dono rising/falling curves ko best balance karta hai; wahan imbalance $600 - 350 = 250$ hai lekin volume choice ko dominate karta hai.

Worked Example 2 — tie-break kaata hai

Worked Example 3 — book mein ek market order

Common mistakes (Steel-manned)

Recall Feynman: 12 saal ke bachche ko samjhao

Socho ek school 350 cookies bech rahi hai. Kuch bacche likhte hain "main 3 rupaye tak dunga," doosre "2 rupaye tak." Kuch bakers kehte hain "main kam se kam 1 rupaye mein bechunga." Teacher sabko line mein khada karti hai aur poochti hai: "Kis single price par SABSE ZYADA cookies bich sakti hain?" Bahut zyada price rakhne par kam bacche khareedenge; bahut kam price par kam bakers bechenge. Ek meethi beech wali price hoti hai jahan sabse bada crowd trade karta hai — aur sabko wahi ek price milti hai. Woh meethi price hi auction price hai.

Active-recall flashcards

Call auction kya output karta hai?

Ek single clearing price aur matched trades ka set, jo executable volume maximise karke nikala jaata hai.

B(p), yaani cumulative demand, define karo.

Saare un buy orders ki total buy quantity jinki limit ≥ p ho; yeh p mein non-increasing hoti hai.

S(p) p mein non-decreasing kyun hoti hai?

Zyada price zyada sellers qualify karta hai (saare sellers jinki limit ≤ p hai), isliye supply price ke saath badhti hai.

Price p par executable volume ka formula.

V(p) = min(B(p), S(p)) — sirf chhoti side trade kar sakti hai.

Auction price kaise chuna jaata hai?

p* = argmax_p V(p), yaani woh price jo matched volume maximise kare.

Max-volume ke baad pehla tie-break kya hai?

Minimum imbalance |B(p) − S(p)|.

Order imbalance I(p) kya hota hai?

I(p) = B(p) − S(p); positive = buy pressure, negative = sell pressure.

Kya B(p*) mein count hone waale saare buyers fill hote hain?

Nahi — sirf V(p*)=min(B,S) shares trade hoti hain; bhaari side ko priority se ration kiya jaata hai.

Continuous trading ka auctions se kya rishta hai?

Yeh batch size 1 ke saath tiny auctions ki ek dhara hai, jo har naye order ko resting book ke against match karti hai.

Market orders cumulative curves mein kaise aate hain?

Limit ±∞ ke saath, isliye woh har price par count hote hain aur volume jodte hain lekin price akele set nahi karte.

Connections

Order Book Dynamics — woh resting book jo B(p) aur S(p) feed karti hai.
Limit vs Market Orders — kyun limits worst acceptable price define karti hain.
Opening and Closing Auctions — din ki boundaries par real-world call auctions.
Price Discovery — auctions price discovery ka discrete engine hain.
Bid-Ask Spread — auction ke dauran single price par collapse ho jaata hai.
Volume-Weighted Average Price (VWAP) — executed auction volume se related benchmark.