The essentials in 30 seconds
- Max pain minimises the modelled total intrinsic value of one selected chain at expiry.
- Open interest counts outstanding contracts; it does not identify holders or their hedges.
- Call and put values across all relevant strikes need the correct multipliers.
- In the example, €100 is the candidate: €10,000 versus €25,000 at €95 and €20,000 at €105.
- A model minimum proves neither a price magnet nor manipulation; new data can change it.
What “max pain” actually calculates
An option can have intrinsic value at expiry. A call has it when the underlying price is above its strike; a put when the price is below. The strike is the contract’s exercise price.
The max-pain calculation asks: At which assumed expiry price is the sum of these values smallest across all outstanding calls and puts in a selected chain? Some market participants examine the figure to describe options positions near expiry.
The dramatic name overstates what the arithmetic establishes. A low intrinsic-value sum is not necessarily the largest real loss for all buyers or the largest profit for all sellers. Premiums paid, share positions and hedges are missing.
Open interest counts contracts, not direction
Open interest (OI) counts outstanding contracts in an options series: one underlying, type, strike and expiry. Every open contract has one long and one short side; it is not counted twice.
Volume instead counts contracts traded during a period. An existing contract can change hands without increasing OI. OI can rise when both sides open new positions and fall when both close them.
High call OI alone does not say everyone expects a rise or reveal dealers’ net gamma. Our comparison of short and gamma squeezes explains why actual positioning matters for hedge flows.
A small model with three strikes
Invented data · not a live options chain
- One hypothetical euro-denominated underlying and one expiry.
- €95 strike: 10 open calls and 40 open puts.
- €100 strike: 20 open calls and 30 open puts.
- €105 strike: 40 open calls and 10 open puts.
- Assumed multiplier: 100 for every contract.
- OI stays fixed; premiums, fees and hedges are excluded.
Each strike has 50 contracts in total, yet their expiry values differ. Picking the strike with the highest OI is no substitute for calculation. We compare expiry prices of €95, €100 and €105. A €5 intrinsic value per unit becomes €500 for one contract at the assumed multiplier.
Change expiry price and inspect each contribution
Select a price. The table shows which calls and puts are in the money and how much they add to the sum. Zero intrinsic value at expiry does not necessarily mean zero lifetime profit or loss.
Invented chain · one underlying · one expiry · euros · multiplier 100 for all contracts · fixed open interest.
| Strike | Call / put OI | Call / put value |
|---|---|---|
| €95 | 10 / 40 | Call: €5,000Put: €0 |
| €100 | 20 / 30 | Call: €0Put: €0 |
| €105 | 40 / 10 | Call: €0Put: €5,000 |
Total intrinsic value at €100: €10,000
Per row: call = max(price − strike, 0) × call OI × 100; put = max(strike − price, 0) × put OI × 100. Add all rows. €100 is the model candidate, not a price forecast. Premiums and hedges are excluded.
Why €100 is the minimum in this chain
At €100, the 10 calls struck at €95 contribute €5 × 10 × 100 = €5,000. The 10 puts struck at €105 contribute another €5,000. Every other series has zero intrinsic value, so the total is €10,000.
At €95, calls are out of the money. The €100 puts contribute €5 × 30 × 100 = €15,000; the €105 puts contribute €10 × 10 × 100 = €10,000. Total: €25,000.
At €105, puts are out of the money. The €95 calls contribute €10 × 10 × 100 = €10,000 and the €100 calls €5 × 20 × 100 = €10,000. Total: €20,000.
For this fixed chain, the sum falls toward €100 and rises afterwards. Thus €100 is the unique model candidate. Two series still have intrinsic value at the minimum: max pain does not mean every option expires worthless.
Why the minimum is no proven price magnet
Adding model payouts does not itself create a share order. Actual prices reflect real buying and selling. News, earnings, large trades and broader market moves can overwhelm options concentrations.
Research on pinning studies prices clustering near a strike under particular positioning and hedging conditions. That is not proof that the global max-pain value of every chain is a reliable expiry target.
- OI changes: opening, closing, exercise and rolling alter the input.
- Positions interact: a call can be part of a spread or share hedge.
- Participants are unknown: OI does not identify holders or their net risks.
- Expiry rules vary: exercise, settlement reference and delivery depend on the product.
- Data quality matters: old snapshots and missing strikes can change the minimum.
A price near the model value proves no manipulation. A price far from it does not invalidate the arithmetic; it shows the static sum need not control the market. Max pain can describe a chain but is insufficient on its own for a trading decision.
Further detail: show assumptions and context
For strike K, call OI C, put OI P, multiplier m and expiry price S, the contribution is m × [C × max(S − K, 0) + P × max(K − S, 0)]. Sum this over the chosen expiry’s strikes.
The function is piecewise linear and convex. Between €95 and €100, its slope in this example is 100 × [10 − (30 + 10)] = −€3,000 per €1 price increase. Between €100 and €105 it is 100 × [(10 + 20) − 10] = +€2,000. The minimum is at €100.
Ties can produce several candidates or a whole flat interval. Different multipliers require separate weighting. Do not silently combine expiries or settlement bases.
This minimum is not identified option writers’ profit optimisation: premiums and hedge results are unknown. Even a complete OI snapshot gives no probability of settlement at the minimum.
What to learn next
Read max pain and the expected move from current option chains.
See strikes, expiry, volume and OI together.
Why actual positioning affects hedge direction.
Separate exercise and delivery from model values.
Glossary
- Open interest
- The count of still-outstanding contracts in an options series.
- Intrinsic value
- The positive exercise or expiry value of an option.
- Pinning
- Observed clustering of expiry prices near a strike under particular conditions.
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