Learn about market making at scale — Hinglish notes

6.5.2 · Stock-Market › HFT & Advanced Concepts

Market making KYA hai?

Yeh kyun exist karte hain? Buyers aur sellers kabhi-kabhi hi ek hi waqt aate hain. MM beech mein khada rehta hai, timing mismatch ko apni inventory mein absorb karta hai, aur badle mein spread leta hai. Inke bina aapko ek natural counterparty ka wait karna padta ("Mujhe abhi AAPL chahiye lekin koi abhi bechna nahi chahta").

"At scale" ka matlab hai: ek modern MM (Citadel Securities, Jane Street, Virtu) tens of thousands instruments quote karta hai, positions milliseconds ke liye hold karta hai, aur din mein millions trades karta hai. Per-trade ka math bahut chhota hai; statistics hi sab kuch hai.

Paisa KAISE banta hai — edge derive karo

Maano ek "true" (fair) price $m$ = mid hai: $m = \frac{P _{a} + P _{b}}{2}$

Half-spread hai $δ = \frac{s}{2} = P_{a} - m = m - P_{b}$ .

Expected profit per round-trip ki derivation. Maano true price move nahi karti. MM ek trader ko $P_{a} = m + δ$ par bechta hai aur doosre se $P_{b} = m - δ$ par kharidta hai. Net cash: $π = (P_{a} - m) + (m - P_{b}) = δ + δ = s$

Lekin do cheezein is edge ko kha jaati hain:

Adverse selection — informed traders tab aapke against trade karte hain jab price aapke favor mein jaane wali ho. Agar ek trader aapse kharidta hai (aapka ask lift karta hai) theek isliye kyunki price upar jaane wali hai, to aapne sasta bech diya.
Inventory risk — agar buys aur sells match nahi hote, to aap ek aisi position carry karte ho jo price moves ke saamne exposed hai.

Adverse selection — scale par asli dushman

Maano $α$ = fill ke turant baad aapke against expected mid-move (price units mein) hai. Tab:

Consequence: jab flow toxic ho tab $δ$ widen karo, jab benign ho (retail) tab tighten karo. Isliye retail-order flow (uninformed) valuable hai — yahi Payment for Order Flow (PFOF) ki wajah hai.

Inventory risk — Avellaneda–Stoikov idea (scratch se)

MM ki wealth ko inventory value samait model karo. $q$ shares hold karo, cash $x$ , mid $m$ . Mark-to-market value: $V = x + q m$

MM ek reservation price $r$ set karta hai = woh price jis par woh inventory hold karne ke liye indifferent ho. Risk aversion $γ$ , price volatility $σ$ , aur time-to-close $T - t$ ke saath:

Phir quotes $r$ ke around symmetrically place kiye jaate hain ( $m$ ke around nahi), aur total spread ek utility-maximizing formula se aata hai: $s^{*} = γ σ^{2} (T - t) + \frac{2}{γ} ln (1 + \frac{γ}{k})$ jahan $k$ order-arrival intensity govern karta hai. Do terms kyun? Pehli term = inventory-risk premium; doosri = fill-rate vs. edge balance karne ke liye chahiye gyi width (ek monopolist ka optimal markup).

Figure — Learn about market making at scale

"At scale" sab kuch kyun badal deta hai

Portfolio inventory variance $N$ roughly-uncorrelated names ke liye: $Var (\sum_{i} q_{i} r_{i}) \approx \sum_{i} q_{i}^{2} σ_{i}^{2} (uncorrelated)$ To edge ke per dollar risk kam hota hai jaise aap names add karte ho — isliye breadth, depth se behtar hai. Correlated names (poora sector) diversify nahi hota; MMs unhe index/futures se hedge karte hain.

Worked examples

Common mistakes

Flashcards

Market maker lagaataar kaun si do prices post karta hai?

Ek bid (buy)

P_{b}

aur ek ask (sell)

P_{a}

— ek two-sided market.

Spread aur half-spread define karo.

Spread

s = P_{a} - P_{b}

; half-spread

δ = s /2 = P_{a} - m = m - P_{b}

jahan

m

mid hai.

Koi price move nahi hone par matched round-trip par gross edge?

Full spread

s = 2 δ

(ek half-spread per leg).

Adverse selection samait realized edge per trade ka formula?

E [π] = δ - α

, jahan

α

aapke against average adverse mid-move hai.

MM ke liye retail (uninformed) order flow valuable kyun hai?

Iska adverse selection kam hota hai (

α \approx 0

), to spread almost pure profit hota hai — PFOF ki basis yahi hai.

Reservation price kya hoti hai aur uska formula kya hai?

Inventory-indifference price

r = m - q γ σ^{2} (T - t)

; aap

m

ke around nahi,

r

ke around quote karte ho.

Long inventory (

q > 0

) hone par quotes kyun skew karte hain?

r < m

hota hai, to aap bid/ask neecha karte ho taaki sellers attract ho aur buyers repel hon, inventory zero par mean-revert ho.

Avellaneda–Stoikov optimal spread mein do terms ka matlab?

γ σ^{2} (T - t)

= inventory-risk premium;

\frac{2}{γ} ln (1 + γ / k)

= fill-rate vs edge markup.

N independent trades ke liye total mean, total variance, aur total std kaise scale karte hain?

Mean

\propto N

, variance

\propto N

(linearly grow karta hai), std

\propto N

Scale par 1/N ki tarah aslmein kya shrink karta hai?

AVERAGE (per-trade) P&L ka variance; total P&L variance

N σ_{π}^{2}

ki tarah grow karta hai.

Scale par total risk badhne ke bawajood "at scale" help kyun karta hai?

Ratio mean/std

= \frac{μ}{σ _{π}} N

grow karta hai — edge, risk se aage nikal jaata hai, to risk-adjusted return improve hota hai.

MMs correlated names ko, jo diversify nahi hote, kaise handle karte hain?

Common factor ko cancellation par rely karne ki bajaye index/future se hedge karte hain.

Recall Feynman: 12-saal ke bachche ko samjhao

Socho ek lemonade stand hai jo kehta hai "Mein tumhare se lembu 9 cents mein khareedunga aur lemonade 11 cents mein bechunga" — hamesha. Har baar kharidne aur bechne par 2 cents milte hain. Woh 2 cents spread hai. Ab agar bahut saare log tumhare paas lembu bechte rehte hain aur koi kharidta nahi, to tera fridge bhar jaata hai (yahi inventory risk hai), isliye extra lembu se peeche chhutne ke liye tu apni prices neeche karta hai. Aur agar ek bahut smart kisan tumhare paas lembu tab bechta hai jab lemon prices girne wali hoti hain — tum bewakoof ban gaye (yahi adverse selection hai). Ek badi lemonade company ek saath har sheher mein ek stand chalati hai. Har sheher kismat ka ek coin-flip hai, to total wobble abhi bhi zyada towns ke saath bada hota hai — lekin tumhara average per town bahut steady aur predictable ho jaata hai, aur tumhara total profit wobble se bhi faster grow karta hai. Chhote 2-cent tukde × zillions of steady trades = asli, reliable paisa.

Connections

Bid-Ask Spread — MM ki edge ka raw material.
Adverse Selection & Informed Trading — spread kyun kamaaya jaata hai.
Inventory Risk & Avellaneda-Stoikov Model — quoting ka math.
Payment for Order Flow (PFOF) — benign flow se paisa banana.
Law of Large Numbers — "at scale" ki statistical backbone.
Order Book Dynamics — jahan quotes actually rehte hain.
Delta Hedging — correlated inventory kaise neutralize hota hai.