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Listed options - mechanics, payoffs, and conventions

Multi-leg strategy payoff builder

Expiration payoff for any combination of legs. Maximum profit, maximum loss, every breakeven, and the payoff across a price range. Every input is encoded in the URL, so a completed position is a link.

Load a worked example, then edit any field. Each of these reproduces a row of the verified reference table at the foot of this page.

Legs

SideType QuantityStrike Premium
Enable JavaScript to edit the position. The formulas, the payoff algebra, and the verified reference table below are static text and do not require it.

Result

Payoff at expiry

The solid line is the position payoff at expiry. The horizontal rule is zero. Dotted verticals mark each breakeven; the dashed vertical marks spot. Shading above the zero line is profit and below it is loss.

Payoff at each strike

Payoff table

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The formulas

Leg payoff

Every figure on this page is the sum of the legs. Each leg contributes its intrinsic value at expiry less the premium paid or received, signed for direction, multiplied by quantity and the contract multiplier. Formulas are stated per share in the reference tables and scaled by the multiplier here.

call leg payoff(S) = d * q * m * ( max(S - K, 0) - premium ) put leg payoff(S) = d * q * m * ( max(K - S, 0) - premium ) stock leg payoff(S) = d * q * m * ( S - entry ) d = +1 long, -1 short q = quantity m = contract multiplier S = underlying price at expiry K = strike

Net debit or credit

The net premium across the option legs only. A stock leg's cost basis is not premium and is excluded, so a covered call built from stock at 98 and a short 105 call at 2.10 shows a 2.10 credit.

net = - sum over option legs of ( d * q * m * premium ) net < 0 debit net > 0 credit

Unbounded profit and unbounded loss

Above the highest strike every option leg is either fully in the money or worthless, so the payoff is linear with a constant slope. The sign of that slope decides whether either extreme is unbounded. Below the lowest strike the payoff is also linear, but the underlying cannot fall below zero, so the downside extreme is finite and occurs at S = 0.

slope above the highest strike = sum of ( d * q * m ) over call legs and stock legs slope > 0 profit unbounded above slope < 0 loss unbounded above slope = 0 payoff flat above the highest strike, both extremes finite

A short call has a positive-quantity short call leg, so the slope is negative and the loss is unbounded. A box spread has offsetting call legs, so the slope is zero, the payoff is a constant, and there is no breakeven at all.

Maximum profit and maximum loss

The payoff is piecewise linear and bends only at a strike, so every extreme sits at a strike, at zero, or at infinity. Evaluating the payoff at zero and at each strike is therefore sufficient once the unbounded cases are excluded.

kinks = { 0 } together with every distinct strike max profit = unbounded if the upper slope is positive, otherwise max payoff over the kinks max loss = unbounded if the upper slope is negative, otherwise min payoff over the kinks where the minimum payoff is above zero the position has no loss at any price

Breakevens

Found by scanning the payoff function for sign changes rather than from a closed form, so an arbitrary combination of legs is handled without a per-strategy rule. Because the payoff is linear between consecutive kinks, walking the kinks in order finds every crossing and the crossing itself is exact by interpolation. A crossing above the highest strike is read off the constant upper slope.

for each consecutive pair of kinks a, b with payoffs Va, Vb: if Va and Vb have opposite signs: breakeven = a + (b - a) * (-Va) / (Vb - Va) above the highest strike Kmax with payoff Vmax and slope u, if u is not zero: breakeven = Kmax - Vmax / u, reported when it exceeds Kmax

The scan finds one breakeven for a ratio spread, two for a butterfly, two for an iron condor, and none for a box spread, from the same code and with no knowledge of what the position is called.

What is excluded

Expiry payoff only. No time value before expiry, no financing or carry, no dividends, no early exercise or assignment, no exercise and assignment fees, no commissions, no bid-offer spread, no margin or collateral cost, and no adjustment for a corporate action changing the deliverable. Legs are assumed to share one expiry, so a calendar or diagonal spread cannot be represented by an expiry payoff at all.

URL parameters

Every input is encoded in the query string, so a completed position is a link. Everything is computed in the browser and nothing is sent anywhere.

ParameterMeaningExample
legsComma-separated position. Each leg is [+|-]qty[c|p|s]strike@price, with c call, p put, s stock. Ratios are expressed by quantity, so [email protected] is two short 105 calls at 1.90. A stock leg takes no strike and is entered at its @price.[email protected],[email protected]
fromLowest underlying price in the payoff table. Defaults to the lowest strike less 20 percent.80
toHighest underlying price in the payoff table. Defaults to the highest strike plus 20 percent.120
stepPrice increment for the payoff table. Defaults to a step that yields about 40 rows.1
multContract multiplier. Defaults to 100.100
spotUnderlying price marked on the diagram. Does not affect any computed figure.100

A 95/100/105 call butterfly:
https://options.wiki/calc/payoff/[email protected],[email protected],[email protected]

A 90/95/105/110 iron condor:
https://options.wiki/calc/payoff/[email protected],[email protected],[email protected],[email protected]

A 100/110 box spread, whose payoff is a constant and which therefore has no breakeven:
https://options.wiki/calc/payoff/[email protected],[email protected],[email protected],[email protected]

Worked examples, verified

Reference values at a 100 contract multiplier. Every row is reproduced by the calculator above; the buttons at the top of the page load each one. Payoffs are at expiry.

StructureInputsNet D/CMax profitMax lossBreakeven(s)
Long callK 100 at 3.20D 3.20Unbounded320.00103.20
Long putK 100 at 2.80D 2.809,720.00 at S=0280.0097.20
Short putK 100 at 2.80C 2.80280.009,720.00 at S=097.20
Covered callS0 98, K 105 at 2.10C 2.10910.009,590.0095.90
Cash-secured putK 95 at 2.40C 2.40240.009,260.0092.60
Bull call spread100 at 3.20 / 110 at 1.10D 2.10790.00210.00102.10
Bear call spread100 at 3.20 / 110 at 1.10C 2.10210.00790.00102.10
Bull put spread95 at 2.05 / 90 at 0.90C 1.15115.00385.0093.85
Bear put spread95 at 4.75 / 90 at 0.90D 3.85115.00385.0091.15
Long straddleK 100, 3.20 + 2.80D 6.00Unbounded600.0094.00 and 106.00
Long strangle95p 1.40 / 105c 1.60D 3.00Unbounded300.0092.00 and 108.00
Long call butterfly95 at 6.40 / 2x100 at 3.40 / 105 at 1.60D 1.20380.00120.0096.20 and 103.80
Long put butterfly105 at 6.40 / 2x100 at 3.40 / 95 at 1.60D 1.20380.00120.0096.20 and 103.80
Iron condor90/95/105/110 at 0.55/1.30/1.45/0.60C 1.60160.00340.0093.40 and 106.60
Iron butterfly95/100/100/105 at 1.30/2.80/3.20/1.60C 3.10310.00190.0096.90 and 103.10
Long call condor90/95/105/110 at 9.75/6.40/1.85/0.40D 1.90310.00190.0091.90 and 108.10
Call ratio 1x2100 at 3.20 / 2x105 at 1.90C 0.60560.00Unbounded110.60
Put ratio 1x2100 at 2.80 / 2x95 at 1.60C 0.40540.008,960.00 at S=089.60
CollarS0 98, 95p 1.50, 105c 2.10C 0.60760.00240.0097.40
Synthetic long100c 3.20 / 100p 2.80D 0.40Unbounded10,040.00 at S=0100.40
Box spread 100/1103.20 / 1.10 / 10.50 / 2.80D 9.8020.00 fixedNoneNo breakeven; payoff constant
Jade lizard90p 2.20, 105c 1.90, 107.5c 1.10C 3.00300.008,700.00 at S=087.00

Published and maintained by · [email protected]. About this reference · options.wiki · the wider network.

A simplified model. Expiry payoff only, one expiry across all legs, European-style treatment with no early exercise or assignment, and no financing, dividends, fees, commissions, spread, or margin cost. Exercise and assignment can occur at any time for American-style contracts and the payoff realised in an account will differ from the expiry payoff shown here. See strategies, exercise and assignment, and margin treatment.

Reference information only. Not investment advice, not a recommendation, and not a solicitation. Options involve substantial risk of loss. Contract terms, margin requirements, and exchange rules change; confirm against the current OCC and exchange rulebooks and your broker's house requirements before trading.