How Max Pain Is Actually Calculated

What Max Pain Actually Sums

Written out, the calculation is four steps and no statistics.

One. Pick a candidate settlement price. Every strike on the board is tested as a candidate in turn.

Two. Value every open call against it. A call at strike K is worth the settlement price minus K if that is positive, and zero otherwise. Multiply that intrinsic value by the open interest standing at that strike.

Three. Value every open put the same way. A put at strike K is worth K minus the settlement price if that is positive, and zero otherwise, again multiplied by the open interest at that strike.

Four. Add the call side and the put side together. That single number is the total value the board would carry at that settlement price. Repeat for every candidate. The candidate producing the smallest total is max pain.

Nothing else enters the calculation. Implied volatility, premium paid, the Greeks, the direction the underlying has been travelling — none of it appears anywhere in those four steps. Max pain is an open-interest-weighted arithmetic exercise and it will produce a number whether or not that number means anything, which is a distinction the last section of this guide comes back to.

One note on units before the example. The totals below are quoted in points multiplied by contracts. Converting them into rupees means multiplying every candidate by the same constant, and a constant multiplier cannot change which candidate is smallest. The units are cosmetic; the ranking is what you are after.

A Worked Example You Can Check

Take a stripped-down NIFTY board: five strikes at 100-point spacing, with open interest in lakh contracts. Real boards carry forty or sixty strikes and every one of them is tested, but the arithmetic is identical and five is enough to follow by hand.

The last three columns answer a different question from the first three. Columns two and three are the open interest standing at that strike. Columns four, five and six are what the whole board would be worth if the underlying settled at that strike.

Take the 24900 row and build it from scratch. Assume the underlying settles at exactly 24900.

The call side. The 24700 calls finish 200 points in the money: 200 × 10 = 2,000. The 24800 calls finish 100 points in the money: 100 × 20 = 2,000. The 24900 calls finish exactly at the money and are worth nothing. The 25000 and 25100 calls finish out of the money and are worth nothing. Call side total: 4,000.

The put side. The 25000 puts finish 100 points in the money: 100 × 10 = 1,000. The 25100 puts finish 200 points in the money: 200 × 10 = 2,000. The 24900, 24800 and 24700 puts all finish at or out of the money and are worth nothing. Put side total: 3,000.

Combined: 7,000. Run the same sum for the other four candidates and you get 14,000 at 24700, 8,000 at 24800, 11,000 at 25000 and 20,000 at 25100. The smallest is 7,000, so max pain for this board is 24900.

The Shape of the Curve Either Side

Plot those five totals and you get a V that is far steeper on one side than the other: 14,000, 8,000, 7,000, 11,000, 20,000. The headline number hides that asymmetry completely, which is why the whole profile is charted rather than just the minimum.

The curve behaves that way for a reason worth understanding. Between any two adjacent strikes, moving the settlement price one point higher costs an extra point on every open call below it, and saves a point on every open put above it. So the total falls while put open interest above outweighs call open interest below, and starts rising the moment that flips. Max pain sits at the strike where the accumulated call open interest underneath first outweighs the accumulated put open interest overhead. Check it against the table: below 24900 there are 30 lakh calls and above it 20 lakh puts, and that is where the curve turns.

A gap of 14 percent to the nearest alternative is a shallow one. Step the other way and 25000 costs 57 percent more than the minimum. This board therefore has a soft floor and a hard ceiling: drifting one strike down is nearly free in settlement terms, drifting one strike up is not. That asymmetry is a more useful piece of information than the headline strike, and it is invisible unless you look at the profile.

When the Profile Is Flat

When the two or three lowest totals sit within a few percent of one another, the strike that happens to be lowest is close to arbitrary. A single block of fresh open interest anywhere on the board can reorder the list, and frequently does, several times in a session.

The practical handling of a shallow basin is to stop treating max pain as a strike and start treating it as a zone. If 24900, 25000 and 24800 all come within a whisker of each other, the honest statement is that settlement is roughly equally cheap anywhere between 24800 and 25000, and quoting 24900 to two decimal places of confidence is false precision.

The runner-up strikes are worth watching in their own right. When the second-lowest total is drifting steadily towards the lowest over successive readings, the open interest distribution is rebalancing in that direction, and the headline strike is likely to move there before expiry. When the runner-up is pulling away, the current minimum is being reinforced.

Distance From Spot and Days to Expiry

Two pieces of context change what the number is worth, and neither of them is part of the calculation.

Distance from spot. A max pain strike sitting a fraction of a percent from where the underlying is trading is inside a normal session's range and is not asking anything of price. A max pain strike two or three percent away is a statement that positioning and price currently disagree. That disagreement resolves in one of two directions, and it is worth being clear that the more common resolution is the open interest distribution moving to where price is, rather than price travelling to where the open interest is.

Days to expiry. The calculation asks what the board would be worth at settlement. With most of a series still to run, the overwhelming majority of the open interest currently on that board will be closed out or rolled long before settlement arrives, so the number is describing a scenario that will never occur with anything like that distribution. It becomes progressively more meaningful as the remaining life shrinks and the book stops changing.

What Max Pain Does Not Tell You

This section matters more than the arithmetic, because the arithmetic is easy and the interpretation is where people go wrong.

It is computed from a distribution that keeps changing. Every contract written or closed alters the sum. The max pain strike you read this morning was calculated from this morning's book, and this afternoon's book is different. It routinely moves several strikes across an expiry cycle. Any conclusion that depends on the number staying put is a conclusion that depends on nobody trading.

It is not a prediction, and there is no mechanism behind it. The calculation identifies where the option book would settle most cheaply. It does not identify anyone with the ability or the intention to take price there. Option writers are thousands of unrelated participants with different books, different constraints and no coordination, and the underlying's price is set by a cash market vastly larger than the option interest sitting on top of it.

It is least meaningful early in a series, for the reason set out above, and it gets discussed most on the expiry session, when the book is at its most concentrated and there is no time left for it to change. That is the one window in which it is at least describing contracts that are genuinely about to settle.

It carries no direction. Spot ten points above max pain and spot ten points below it produce the same strike. Anything directional you attach to it is coming from you, not from the number.

Events override it entirely. A result, a policy decision or an overnight global move will reprice the underlying without any regard for where option open interest happens to sit. Max pain is most often discussed as an expiry-day reference precisely because it is a quiet-session phenomenon, and a session with a catalyst in it is not a quiet session.

What it is genuinely useful for is narrower and more honest: a single reference level derived from the whole open interest distribution, to be read next to the walls that distribution also produces. When the max pain strike, the heaviest call strike above spot and the heaviest put strike below spot all point at the same neighbourhood, positioning is at least internally consistent. When they scatter, the book is telling you it has no settled view.

The distribution feeding all of this is the same one shaded on the heatmap, and the OI heatmap guide covers how to read its shape directly. For what the open interest columns themselves measure, and how a change in open interest is read against price, start with the open interest guide.