Learn weekly - monthly options expiry effects — Stock-Market notes

WHAT is happening

WHY expiry moves price (first principles)

Intuition Follow the hedger — sign of gamma decides everything

A hedger who is delta-neutral must re-hedge as spot moves. Whether that hedging calms or fuels the move depends on the sign of their gamma:

Long gamma (option BUYER hedging): as spot rises, delta rises → to stay neutral they sell into the rally; as spot falls, delta falls → they buy the dip. This is buy-low / sell-high → it absorbs moves and can pin price near the strike.
Short gamma (option WRITER hedging): as spot rises, their (short) delta grows more negative → to stay neutral they buy into the rally; as spot falls they sell. This is buy-high / sell-low → it chases and amplifies the move → breakouts.
Near an ATM strike close to expiry, gamma explodes for both sides, so whichever side dominates the market's net-hedging flow determines the day: net long gamma → pinning; net short gamma → violent trend.
When a high-OI wall is breached, short-gamma hedgers are forced to chase hard → explosive gamma unwind.

Steel-man note: the naive claim "writers pin the price" is only true when the market-maker/dealer complex is net long the gamma they've warehoused. Empirical pinning near high-OI strikes typically reflects dealers being net long options at those strikes (buy-low/sell-high), not writers amplifying moves.

Deriving Max Pain from scratch

We want the spot price $S$ at expiry that causes the least total payout to option buyers (equivalently, the most pain — hence "max pain").

Step 1 — payoff of one option at expiry.

A Call at strike $K$ pays the buyer: $\max(S-K,\,0)$ .
A Put at strike $K$ pays the buyer: $\max(K-S,\,0)$ .

Why this step? At expiry there's no time value left — only intrinsic value remains. That's the definition of intrinsic value.

Step 2 — total buyer payout across all strikes. Let $\text{OI}^{C}_K$ and $\text{OI}^{P}_K$ be open interest (contracts) at each strike. Total cash the writers must pay (per unit lot):

\text{Pain}(S)=\sum_{K}\Big[\text{OI}^{C}_K\cdot\max(S-K,0)\;+\;\text{OI}^{P}_K\cdot\max(K-S,0)\Big]

Why this step? Every rupee a buyer receives is a rupee a writer loses. Writers (usually well-capitalized, often institutions) have incentive/ability to nudge $S$ toward low-payout zones.

Step 3 — minimize.

S_{\text{maxpain}}=\arg\min_{S}\ \text{Pain}(S)

Why this step? The strike minimizing total intrinsic payout is where the most options die worthless. Empirically, price often drifts toward this level into expiry (pinning) when dealers are net long gamma there, though it is a tendency, not a law.

Figure — Learn weekly - monthly options expiry effects

HOW to trade around it (the 80/20)

Worked Examples

Worked example Example 1 — Computing Max Pain

NIFTY, only three strikes with OI (in lots):

Strike $K$	Call OI	Put OI
24000	100	20
24100	60	60
24200	20	120

Test $S=24100$ :

Calls pay: $100(24100-24000)^+ + 60(0)+20(0)=100\times100=10000$
Puts pay: $20(0)+60(0)+120(24200-24100)=120\times100=12000$
Pain $=22000$ .

Test $S=24000$ :

Calls: $100(0)+60(0)+20(0)=0$
Puts: $20(0)+60(24100-24000)+120(24200-24000)=60(100)+120(200)=6000+24000=30000$
Pain $=30000$ .

Test $S=24200$ :

Calls: $100(200)+60(100)+20(0)=20000+6000=26000$
Puts: $0$ . Pain $=26000$ .

Minimum pain is at $S=24100$ (22000). Why? Balanced OI → if dealers are net long gamma here, price is likely pinned near 24100 into expiry.

Common Mistakes

Recall Feynman: explain to a 12-year-old

Imagine a see-saw with a magnet in the middle. Some players own bets and act like the magnet — every time the see-saw tips, they gently push it back to the center number, so it stays put ("pinning"). Other players sold bets and act the opposite — when the see-saw tips, they push it further the same way, making it swing wildly. On the last day both effects get super strong. Which group is bigger decides whether the price stays stuck on a magic number or suddenly rockets away.

Active Recall

What is options expiry?

The date/time a contract stops existing; it settles if ITM (has intrinsic value) or expires worthless if OTM.

Define Max Pain.

The spot price at expiry that minimizes total intrinsic payout to option buyers, i.e. makes the most options expire worthless.

Write the Max Pain objective.

S_{maxpain}=\arg\min_S \sum_K [OI^C_K(S-K)^+ + OI^P_K(K-S)^+]

Which sign of gamma causes pinning?

Long gamma — the hedge is buy-low/sell-high, which absorbs/dampens moves and pins price toward the strike.

Which sign of gamma causes breakouts?

Short gamma — the hedge is buy-high/sell-low, which chases and amplifies moves.

Do option writers hedging pin the price?

No — writers are short gamma (buy-high/sell-low), which amplifies moves. Pinning comes from net long-gamma dealers/buyers.

What causes an explosive move on expiry day?

A high-OI wall is breached and short-gamma hedgers are forced to chase (buy-high/sell-low) → gamma unwind amplifies the move.

Why is buying far-OTM weekly options on expiry usually a losing game?

Savage theta decay + low probability of finishing ITM → negative expected value; writers are systematically on the other side.

Difference between weekly and monthly expiry effects?

Monthly has much larger OI, rollovers, and index rebalancing → bigger trends; weekly has faster theta and cheaper, high-turnover premiums.

Is Max Pain a guarantee?

No — it's a probabilistic magnet that mostly holds when dealers are net long gamma near the strike; news/large flow/wall breaks override it.

What is Open Interest (OI)?

The number of option contracts currently open (not yet closed or expired).

Connections

Options Greeks — Delta & Gamma
Theta Decay & Time Value
Open Interest & Volume Analysis
Delta Hedging by Market Makers
Gamma Exposure (GEX) & Dealer Positioning
Index Rebalancing Effects
When to Trade — Timing & Sessions
Implied Volatility & IV Crush

Concept Map

Hinglish (regional understanding)

Intuition Hinglish mein samjho

Expiry day pe options ka game asli maze ka hota hai. Sabse important baat: hedging price ko pin karegi ya breakout degi, yeh depend karta hai gamma ke sign pe. Jo trader options kharidta hai woh long gamma hota hai — uska hedge buy-low / sell-high hota hai, jo moves ko dabata hai aur price ko strike ke paas chipka deta hai (pinning). Jo bechta hai (writer) woh short gamma hota hai — uska hedge buy-high / sell-low hota hai, jo move ko aur tez kar deta hai (breakout).

Ek galatfehmi door karo: log kehte hain "writers price ko pin karte hain" — yeh galat hai. Writers short gamma hote hain, unka hedging move ko badhata hai, pin nahi karta. Pinning tab hoti hai jab dealer/buyer complex net long gamma ho us strike pe. ATM strike aur expiry najdeek ho to gamma dono taraf bahut bada ho jaata hai, isliye jo side bhaari padti hai wahi din ka behavior decide karti hai.

Max Pain ka simple matlab: woh price jahan sabse zyada options bekaar expire ho jaayein, yaani buyers ko sabse kam paisa mile. Formula bas intrinsic value ka total minimize karna hai — call ka $(S-K)^+$ aur put ka $(K-S)^+$ , OI se multiply karke. Par yeh guarantee nahi — sirf tab tak magnet hai jab tak dealers net long gamma hain. Wall toot gaya to short-gamma hedgers chase karte hain aur price rocket ki tarah bhaagta hai (gamma unwind).

Practical 80/20: expiry pe theta bahut fast hai, isliye sasti OTM weekly options kharidna aksar loss ka sauda hai. Max Pain aur high-OI strikes ko magnet/wall samjho. Mnemonic yaad rakho: "Long gamma PINs, Short gamma SPINs". Monthly expiry me OI aur rollover zyada, isliye trend bade aur saaf ho sakte hain.

Test yourself — When to Trade — Timing & Sessions

Connections