What Is Max Pain in Options? How It Is Calculated and What It Shows

Max pain is the expiry price at which the options still open on an underlying would pay their holders the least in total, found from open interest by strike.

The number is quoted widely for equity options and for crypto options on Bitcoin and Ethereum, often with a claim attached: that the price gets drawn toward it into expiry. The calculation itself is simple arithmetic on a snapshot of open contracts, and it says nothing about where the price will settle. This page covers how max pain is calculated, a worked example, what the calculation assumes, what research on prices clustering at strikes has found, how Kresmion computes it for crypto options, and what the figure cannot tell you. It is descriptive throughout.

How max pain is calculated

If calls, puts and strikes are new to you, start with what a call option and a put option are. At expiry an option is worth only its intrinsic value: a call pays the settlement price minus the strike when that is positive, and a put pays the strike minus the settlement price when that is positive. Everything else pays nothing.

Max pain applies that rule to the whole board for one expiry:

1. Take every strike listed for the expiry, with the open interest on its calls and its puts. 2. Pick a candidate settlement price, usually one of the listed strikes. 3. For each call strike below the candidate, multiply the amount it finishes in the money by its open interest. Do the same for each put strike above the candidate. Add everything up. That total is what all open contracts would pay their holders if the underlying settled exactly there. 4. Repeat for every candidate. The candidate with the smallest total is the max pain strike.

The name comes from the holders' side: at that strike, option buyers taken together collect the least, so it is the point of maximum pain for them. The arithmetic needs no pricing model, no implied volatility and no assumption about the future.

A worked example

Take a hypothetical underlying near 100 with five strikes on one expiry, each contract covering one unit of the underlying. The open interest is invented for illustration.

Now settle the expiry at each strike in turn and total what the calls and the puts would pay.

At 100, for example, the calls struck at 90 and 95 finish in the money: 10 times 50 plus 5 times 150 is $1,250. The puts struck at 105 and 110 finish in the money: 5 times 100 plus 10 times 50 is $1,000. The total, $2,250, is the lowest of the five, so 100 is the max pain strike.

Two features of the result are typical. The largest call open interest sits at 110 and the largest put open interest at 90, yet max pain lands between them, because the calculation weighs how far each strike would finish in the money, not just how many contracts sit there. And the total climbs steeply on both sides of the minimum, since every strike crossed adds a new layer of contracts that pay.

What the calculation assumes

Max pain is often explained as the price where option sellers, usually described as market makers, lose the least, with the suggestion that they have both the motive and the means to steer the price there. The arithmetic does not support that reading on its own, for four reasons.

• It ignores premium. A writer's result is the premium collected minus the payout. Max pain counts only the payout, so it is not the point where any actual writer does best.
• It does not know who holds which side. Open interest counts contracts outstanding, with one buyer and one seller behind each, and does not say whether the seller is a dealer, a fund writing covered calls or another investor. Dealers can be net long options at some strikes and short at others.
• It ignores hedging. A market maker that sold options usually hedges the delta in the underlying, so its result at expiry depends on the whole hedged book, not on the intrinsic value of the options alone. How that hedging works is in dealer gamma exposure.
• It is a snapshot. Open interest changes every day as contracts are opened and closed, so the max pain strike can move from one day to the next without any change in price.

What research on pinning has found

There is evidence that prices can cluster at strikes around expiry, and it is worth stating precisely because it is often cited in support of max pain. Sophie Ni, Neil Pearson and Allen Poteshman, in the Journal of Financial Economics in 2005, reported that on expiration dates the closing prices of stocks with listed options cluster at option strike prices, and they provided evidence that hedge rebalancing by option market makers and stock price manipulation by firm proprietary traders contribute to the clustering. Marco Avellaneda and Michael Lipkin, in Quantitative Finance in 2003, modeled how delta hedging by market makers, when open interest on a contract is unusually large, can push a stock toward that strike, with a probability of pinning that depends on volatility, time to maturity, open interest and price impact.

Both describe clustering at strikes; in the model it comes from delta hedging of unusually large open interest, which is close to what the call and put walls page describes when dealers hold long gamma near a strike. Neither defines nor tests the max pain strike, which can sit away from the strikes with the most call or the most put open interest, as the example above shows. Evidence that prices sometimes settle near heavily traded strikes is a different claim from evidence that they move toward the strike that minimizes total payout.

Max pain in crypto options

Max pain is quoted heavily for Bitcoin and Ethereum options, where large expiries draw attention. The calculation is the same. Deribit, a crypto options exchange, describes its options as European style, exercised automatically at expiry and cash settled, so the dollar value of the payout at expiry is the intrinsic value the calculation uses.

Kresmion computes max pain for BTC and ETH options, refreshed about every 30 minutes, and shows it in the options panel of its crypto derivatives page, which opens with a free account, alongside at the money implied volatility, a put minus call skew reading, the put/call open interest ratio and total options open interest. The candidates are the strikes listed for the nearest expiry, and each strike is weighted by its open interest in contracts. Two details matter when reading it. The max pain figure covers only that nearest expiry, while the put/call ratio and total open interest in the same panel cover every listed expiry. And the nearest expiry can be a short-dated contract holding a small share of all open interest, so the figure can change when that expiry rolls off and the next one becomes nearest. For what the put/call ratio measures, see options skew and the put/call ratio.

What max pain cannot tell you

Max pain describes how open interest is distributed across strikes for one expiry. It does not say where the price will settle, how likely any settlement price is, or who would gain or lose at each strike, because it leaves out premium, hedging and the identity of the holders. It is not a probability either. A risk-neutral distribution of settlement prices can be backed out of option prices, which is what Kresmion's options-implied probability tool does for a set of US listed underlyings, and that distribution includes a risk premium and is not a forecast. And any one reading is a snapshot of open interest that the next session can reshape. Kresmion shows the figure as a description of the current board and does not flag or forecast settlement prices.

Key takeaways

Frequently asked questions

Does the price move toward max pain before expiry?

Max pain itself does not show that. Research has found that stock closing prices can cluster at strike prices on expiration dates, and links that partly to market maker hedging, but those studies look at strikes in general, not at the max pain strike. Nothing in the calculation requires the settlement price to land near it, and the figure itself moves as open interest changes.

Is max pain the price where market makers make the most money?

Not necessarily. The calculation counts only what options pay at expiry. A market maker's result also depends on the premium it collected, on whether it is long or short at each strike, and on the shares or futures it holds as a hedge, none of which appear in open interest.

How is max pain different from the put/call ratio?

The put/call ratio divides put activity by call activity, so it summarizes the balance between the two sides in one number. Max pain uses the full distribution of open interest across strikes and finds the settlement price that minimizes total payout. They answer different questions, and on Kresmion's crypto panel they also cover different expiries.

Why does max pain change from day to day?

Because open interest changes. New contracts are opened, old ones are closed, and expiries roll off, each of which reshapes the board the calculation runs on. A change in max pain can happen with no change in the underlying price.

This page is information, not investment advice.

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Source: Ni, Pearson and Poteshman, "Stock price clustering on option expiration dates", Journal of Financial Economics 78(1), 2005, pp. 49 to 87, https://experts.illinois.edu/en/publications/stock-price-clustering-on-option-expiration-dates/ ; Avellaneda and Lipkin, "A market-induced mechanism for stock pinning", Quantitative Finance 3(6), 2003, pp. 417 to 425, https://econpapers.repec.org/article/tafquantf/v_3a3_3ay_3a2003_3ai_3a6_3ap_3a417-425.htm ; Deribit Insights, "What is an Options Contract", https://insights.deribit.com/education/what-is-an-options-contract/ ; Kresmion crypto options summary (BTC and ETH). The worked example uses invented open interest.

Kresmion Research.