Max Pain in Options: Formula, Calculation and Its Limits

Max pain is the strike price at which option holders would collect the least money if the stock finished there at expiry. It is calculated from open interest alone. Vyreon reports it for the next expiry and the next monthly expiry, as a description of where open positions sit, not as a price prediction.

What Is Max Pain?

At expiry, a call pays its holder the amount the stock finishes above the strike, and a put pays the amount it finishes below. For any possible closing price, you can add up what every open contract would pay. Max pain is the strike where that total is smallest: where option buyers, as a group, would collect least and option writers would pay out least.

Max Pain Formula

For each listed strike K* taken as the expiry price:

Total payout(K*) = Σ call OI × max(0, K* − K) + Σ put OI × max(0, K − K*)

summed over every strike K of that expiry. Max pain is the K* with the smallest total.

Illustrative example: an expiry has strikes 95, 100 and 105. Open calls are 100, 300 and 500; open puts are 400, 300 and 100. Per share:

At 95: puts pay 5 × 300 + 10 × 100 = 2,500; calls pay nothing.
At 100: calls pay 5 × 100 = 500; puts pay 5 × 100 = 500; total 1,000.
At 105: calls pay 10 × 100 + 5 × 300 = 2,500; puts pay nothing.

Max pain is 100.

How Vyreon Measures It

Next expiry: the first listed expiry after the session.
Monthly expiry: the first standard monthly expiry after the session (the third Friday, or the Thursday before when that Friday is a market holiday).
Candidates are the listed strikes of that expiry; if two strikes tie, the lower one is reported.
Open interest is as of the previous session's close, the latest the clearing process publishes.
Vyreon shows the max pain strike, its distance from the closing price, and the open interest in that expiry, so you can see how much positioning the figure rests on.

Is Max Pain Theory Reliable?

"Max pain theory" claims prices tend to drift toward the max pain strike into expiry, with option writers or dealers said to push the price there. Treat that with caution:

Open interest does not show who wrote or bought each contract, or whether positions are hedged. The idea that writers want, or are able, to pin the price is an assumption, not something the data shows.
Max pain can sit near the current price simply because open interest is concentrated at nearby strikes. Finding the two close together is not evidence of pinning.
Open interest changes every day as positions open and close, so max pain moves too.
A thinly traded expiry can produce a max pain strike that rests on very few contracts.

What It Does Not Tell You

Where the price will finish. Max pain is a calculation over open positions, not a forecast or a target.
Who would gain or lose. Contracts can be parts of spreads or hedges, so "pain" to holders is a simplification.
Anything about expiries other than the two shown.

Sources

Sophie Xiaoyan Ni, Neil D. Pearson and Allen M. Poteshman, "Stock Price Clustering on Option Expiration Dates", Journal of Financial Economics (2005): closing prices of optionable stocks cluster at strike prices on expiration dates, with evidence pointing to hedge rebalancing by option market makers and manipulation by proprietary traders. It studies strike prices in general, not the max pain strike.
John C. Hull, Options, Futures, and Other Derivatives (Pearson, many editions): option payoffs at expiration.

Max pain is a market convention; we know of no peer-reviewed source establishing that prices move toward it.