Tools

Structured Payoff: Floor, Cap and Participation

A structure promises a floor under your losses, a cap over your gains and a participation rate between them. How much upside does the floor actually cost, and at which index outcomes does holding the index directly pay more?

Three numbers describe this kind of structure — a floor, a cap and a participation rate — and they are almost always quoted one at a time. They are not independent. Where the cap starts to bind, where it starts to cost you, where the floor starts to bind and where the protection has actually paid for itself are four different index outcomes, and only at a participation rate of exactly one hundred per cent do any of them coincide. This page computes all four, from your own terms.

What this tool does not decide

Whether to buy anything. A payoff is a description of a promise, not a verdict on it.
What the index will do. No probability appears anywhere. You state where the index finishes; the model says what the structure pays if it does.
What the structure is worth. A payoff is not a value. Pricing one would need a market this page does not have, and nothing here says whether the terms are fair or the price reasonable.
Whether the issuer will pay. Credit risk sits entirely outside this arithmetic, and it is the risk that turns every figure here into nothing at once.
Which structure you hold. This tool names no issuer, product, wrapper or index, ships none and fetches none. Every figure is yours.
Anything about tax, in any jurisdiction.

Your figures

The interactive calculation runs in your browser and needs local JavaScript, which is currently switched off. Activating the Calculate button does nothing at all: no request is sent and nothing is submitted.

Everything else on this page works without it. The model, the formulas, the timing convention, the worked example, the assumptions and the limitations are all in the methodology below, and the companion explainer covers the mechanism in full.

The structure, in its own terms

Everything here is yours. Nothing is sent anywhere, nothing is stored, and no issuer, product, index or price is looked up. There is no field for how much you are investing, because the payoff scales exactly with the amount — every figure below is a percentage of whatever you put in.

What the structure is bounded by

All three are sold and they pay very differently. A structure with a cap and no floor participates in a fall without limit and stops growing on the way up, which is the combination readers are least often told about plainly. This control has no default because choosing for you would answer the question you came to ask.

The participation rate

How much of the index move the structure passes on between its bounds. 100 is one-for-one; 120 passes on more than the index moved; 80 passes on less. It is the parameter that decides where the bounds actually start to matter, and it is the one most often quoted on its own.

The floor

The least the structure can pay, as a percentage of what you put in. Enter -10 for a structure that cannot lose you more than a tenth, or 0 for one that returns your money and no less. Enter it as a negative number — a floor above zero would promise a gain whatever the index did, which is a different instrument.

The cap

The most the structure can pay, as a percentage of what you put in. Enter 8 for a structure capped at eight per cent over the term. Note that this is the cap on the payoff, not on the index: at a participation rate other than 100 they are reached at different index outcomes, and both are published in the result.

Where the index finishes

The index outcome you want the payoff for, over the whole term. This is a number you state and not one this page predicts — there is no probability anywhere in this arithmetic, and no outcome here is more or less likely than any other. The result also publishes the whole payoff across a range, so you can see where yours sits.

Result

This page computes a structure with a floor: a level the payoff stops falling at, and stays at however much further the index falls. The word “buffer” is also used for a different arrangement — one that absorbs the first stretch of a fall entirely and then passes the rest through in full. The two are not variations on each other. At a small fall the absorbing arrangement pays more; at a large one the floor pays more, and by a widening margin. If your term sheet describes losses resuming beyond a threshold rather than stopping at one, this is not the mechanism you hold and nothing here describes it.

Enter your figures above and select Calculate. Nothing is sent anywhere: the calculation runs in this browser, and no value is stored, shared or placed in the address bar.

Where the floor starts to bind, as an index outcome: Not yet calculated
Where the cap starts to bind, as an index outcome: Not yet calculated
Below this index outcome, the structure pays more than the index: Not yet calculated
Above this index outcome, holding the index would have paid more: Not yet calculated
What the structure pays you: Not yet calculated
Against simply holding the index: Not yet calculated
The rise you did not receive: Not yet calculated
The fall you did not take: Not yet calculated
Which stretch of the payoff you landed on: Not yet calculated

This is the payoff function and nothing else: what the structure pays for a given index outcome over the term, as a share of what you put in. It holds no issuer, no term sheet, no notional, no currency, no credit risk and no index. It carries no time — the payoff depends on where the index finishes and on nothing about how it got there — so a structure whose payoff depends on the path is a different mechanism and is not this one with different numbers.

No outcome on this page is more or less likely than any other. There is no probability, no distribution, no volatility and no expected return anywhere in this arithmetic: the index outcome is a number you state, and every figure is what the structure pays if that is where the index finishes. A payoff is not a value either — pricing one would need a market this page does not have, and nothing here says whether the structure is worth what it costs.

How this is worked out

Two arrangements are sold under one word

This page computes a structure with a floor: a level the payoff stops falling at and stays at, however much further the index falls. The word "buffer" is also used for an arrangement that absorbs the first stretch of a fall entirely and then lets the rest through in full. They are not variations on each other, and the difference grows with the size of the fall.

A floor of −10% and an absorbing band of 10%, both at one-for-one participation. At a small fall the absorbing arrangement is ahead. At a large one the floor is ahead, by a widening margin. This page computes the first column.
What the index does	A floor at −10% (this page)	An absorbing band of 10% (not computed here)
The index falls 5%	You lose 5% — the floor has not been reached	You lose nothing — the fall is inside the absorbed band
The index falls 10%	You lose 10% — the floor binds exactly here	You lose nothing — the fall is exactly the absorbed band
The index falls 30%	You lose 10% — the floor holds and the rest is not yours	You lose 20% — the first tenth is absorbed and the rest passes through
The index falls 60%	You lose 10% — the floor still holds	You lose 50% — the gap between the two is now five times the band

If your term sheet describes losses resuming beyond a threshold rather thanstopping at one, this is not the mechanism you hold and nothing on this page describes it.

The payoff, in one line

Writing x for where the index finishes, p for the participation rate,f for the floor and c for the cap, all as fractions over the term:

payoff(x) = min( max( p × x, f ), c )

Three straight stretches with two bends in them, and the whole of the structure's behaviour is in where the bends fall. An index that finishes exactly where it started pays exactly nothing, which is what makes the floor at or below zero and the cap above it — not a view about which products exist, but the condition under which this is an index-linked structure rather than a deposit.

Four index outcomes, and no two of them are the same question

This is what the calculator adds, and it is the reason a paragraph could not carry the answer.A cap starts binding at one index outcome and starts costing at another. Between them the structure has stopped growing and is still ahead of an index that has not yet caught it. The same holds downward, mirrored — and at a participation rate above one it is the wrong way round from most readers' intuition, because the floor binds above the outcome at which the protection has paid for itself.

The four quantities published on every result. Only at a participation rate of exactly 100% do the first and third coincide, and the second and fourth.
The outcome	Where it is	What it means	What it is not
Where the floor starts to bind	floor ÷ participation	Below this index outcome the payoff stops moving	Equals the floor only at a participation rate of exactly 100%
Where the cap starts to bind	cap ÷ participation	Above this index outcome the payoff stops moving	Equals the cap only at a participation rate of exactly 100%
Below this, the structure leads	the floor, or zero if participation is under 100%	Where the protection has actually paid for itself	Not the same as where the floor binds, unless participation is 100%
Above this, the index leads	the cap, or zero if participation is under 100%	Where the cap has actually cost you something	Not the same as where the cap binds, unless participation is 100%

What the comparison is against

Holding the index directly, and nothing else. Not cash, not a deposit, not another investment. The comparison is fixed and narrow on purpose: a structure of this kind is sold as a way of holding an index differently, so the only counterfactual the mechanism licenses is holding it. Every "against the index" figure on this page is that comparison and no other.

What you enter

What bounds the structure: Which of the three shapes you hold. There is no default
Participation rate: A percentage of the index move, above zero
The floor: A percentage over the term, at or below zero. Only where the structure has one
The cap: A percentage over the term, above zero. Only where the structure has one
Where the index finishes: A percentage over the term. Yours to state, not this page to guess

The limits this payoff imposes on itself

A payoff function is a complete description of one thing and no description at all of several others. Each of these is a way the figures above can be right and still not be what you receive.

A structure is a promise by an issuer, and this arithmetic assumes the promise is kept. Credit risk sits entirely outside it, and it is the risk that turns every figure on this page into nothing at once.
This is a payoff and not a value. What the structure would cost to buy, what it is worth today, and whether the terms are fair are three different questions and none of them is answered here — pricing one would need a market this page does not have.
Charges inside the wrapper are not modelled. Where they exist they come out of what you receive, so the real payoff sits below every figure here.
Income given up is not modelled. Holding an index directly usually pays dividends and holding a structure written on it usually does not, so the against-the-index column understates what direct holding would have returned.
The payoff depends on where the index finishes and on nothing about how it got there. A structure with a barrier, an averaging window, an observation date or an autocall feature is path-dependent, is a different mechanism, and is not this one with different numbers.
Nothing here is a probability. No outcome on this page is more or less likely than any other, and the model holds no distribution, no volatility and no expected return at all.

What is not modelled

credit risk — the structure is a promise by an issuer, and this arithmetic assumes the promise is kept
the price of the structure, its fair value, or whether it is worth what is being asked for it
any charge, commission, spread or distribution fee inside the wrapper
the path the index takes, including any barrier, averaging window or observation date
income given up by holding the structure rather than the index, including dividends
early redemption, autocall features, and what happens if you sell before the term ends
the probability of any outcome, which is not a quantity anywhere on this page
tax, in any jurisdiction

A structure and the index it is written on are two uses of the same money, and they are only comparable once the basis is stated.The explainer on comparing two financial uses of money covers that one, and needs no JavaScript at all.

Go deeper

The nearest published mechanism
How to Compare Two Uses of Money Without Fake Certainty
Why opportunity cost only exists relative to a real alternative, what makes a comparison like-for-like, why a higher annual rate can start behind, and why the option that ends higher is not automatically the one to choose.
A structure and the index it is written on are two uses of the same money. The comparison only means anything once the basis is stated, which is what the against-the-index column on this page is doing.
Read the explainer: How to Compare Two Uses of Money Without Fake Certainty

Calculation model and corrections

Calculation model: Buffered Payoff v1.0
Last reviewed: 27 August 2026
The floor: A level the payoff stops falling at and stays at, however much further the index falls. Not an absorbing band that soaks up the first part of a fall and then lets the rest through — that is a different arrangement and this page does not compute it
The comparison: Holding the index directly, and nothing else. Not cash, not a deposit, not any other investment: the structure is sold as a way of holding an index differently, so that is the only counterfactual the mechanism licenses
Every figure: A return over the term as a whole, as a percentage of what you put in. There is no amount and no currency, because the payoff scales exactly with the amount and stating one would inform nothing
Time: Absent. The payoff depends on where the index finishes and on nothing about how it got there, so there is no schedule, no path, no averaging window and no observation date
Binding and costing: Two different index outcomes whenever the participation rate is not exactly one. Both are published, under names that say which is which
The origin: An index that finishes where it started pays nothing. That is what makes the floor at or below zero and the cap above it, rather than a view about which products exist
The sampled range: Fixed at a fall of 50% to a rise of 50% for every reader, so two structures compared on this page are read off the same grid. A kink outside that range is still published as a figure
Excluded: Credit risk, price, charges, dividends, early redemption, probability and tax
Rounding: Display only; intermediate values remain unrounded

Correction history

The qualification record that commissioned this model calls the upper kink “where the cap starts costing”. It is the one place the corpus is loose, and the model does not reproduce it: a cap starts binding at one index outcome and starts costing at another, and they coincide only at a participation rate of exactly one. Both are computed and both are published under names that cannot be confused, rather than the looser phrase being carried through because it was the commission’s own.
The word “buffer” was reviewed against the frozen record before any code was written, and the reading was recorded rather than assumed. The record describes a payoff that is “flat outside” its bounds, which is a floor; an absorbing band is flat *inside* one. The other mechanism is named on this page as an arrangement this arithmetic does not describe, because a reader who holds it would otherwise read every figure here as being about theirs.