Payoff across settlement prices
Each row is a possible price at expiry. The tent peaks at the middle strike; one side flattens into profit (no risk there) and the other into the capped loss. The rows are shaded by zone and the break-evens are marked.
| Price at expiry | Move | P&L ($) | Zone |
|---|
Lopsided on purpose
A broken-wing butterfly is a butterfly that has decided which way it is willing to be wrong. You buy one call low, sell two at the middle and buy one high, just like a normal butterfly — but you push one of the outer strikes further out, skipping a strike. That asymmetry is the whole point. Widen the near wing and the far side of the payoff flattens out above zero, so price can run away in that direction and you still make money; all the risk collapses onto the other side, where the loss is capped but real. Better still, the lopsided structure often lets you open the trade for a credit instead of a debit, so you are paid to put it on and simply keep the credit if price stays on the safe side. The middle strike is still where you make the most. The honest way to read it is to look at three numbers together: the credit or debit, which side carries the risk, and the probability of finishing in profit. A credit broken-wing with a safe downside and a 65% chance of profit is a very different animal from a debit one that pays off only on a precise pin. If you want the symmetric version, use the butterfly spread calculator; to collect premium inside a range with two defined wings, price an iron condor; and to see the delta and theta that move the position before expiry, use the options greeks calculator.
The math
Label the three strikes A (lower, long one call), B (middle, short two calls) and C (upper, long one call), with A < B < C. The near wing is Wn = B − A and the far wing is Wf = C − B; a broken-wing butterfly has Wn ≠ Wf. Write the net premium as P, positive for a debit paid and negative for a credit received. The intrinsic value of the combo at settlement S is V(S) = max(S−A,0) − 2·max(S−B,0) + max(S−C,0), and the profit is V(S) − P.
The peak sits at the middle strike, where V(B) = Wn, so the maximum profit is Wn − P. Below A the value is flat at 0, giving a profit of −P (a credit is kept, a debit is lost). Above C the value is flat at Wn − Wf, giving a profit of (Wn − Wf) − P. Whichever of those two tails is positive is the risk-free side; the other holds the maximum loss, equal to P + max(0, Wf − Wn). The two break-evens are found on the sloped segments: the lower one at A + P (on the rising A→B leg) and the upper one at 2B − A − P (on the falling B→C leg), and only the one facing the risk side actually exists. The probability of profit is the chance S lands in the profit region, estimated from a lognormal move whose one-standard-deviation spread is σabs = S · vol · √(days ÷ 365), using the normal CDF Φ. This ignores drift, carry, early assignment and pre-expiry mark-to-market, so treat the probability as a planning estimate.
FAQ
What is a broken-wing butterfly and how is it different from a regular one? A broken-wing butterfly is a butterfly with one wing deliberately made wider than the other — you skip a strike on one side, which is why it is also called a skip-strike butterfly. A standard butterfly has two equal wings and always costs a small debit; the broken-wing version shifts the far strike so the structure becomes lopsided. That single change does two useful things. First, it can often be opened for a net credit instead of a debit, meaning you take money in when you put the trade on. Second, it removes the risk on one side entirely: whichever way you skipped the strike, the payoff there flattens out at a profit rather than a loss. The price you pay is that all the risk piles onto the other side, capped but larger than a plain butterfly's. So a broken-wing butterfly is the trade you use when you have a directional lean — you are fine being wrong in one direction but want protection or income if you are wrong in the other.
How can a broken-wing butterfly have no risk on one side? It comes down to the residual value of the option combo at the extremes. In a call broken-wing butterfly you are long one call low, short two at the middle, and long one high. Far below the lowest strike every option is worthless, so your profit or loss there is just the credit you took in or the debit you paid — a flat line. Far above the highest strike the long and short calls net out to a fixed intrinsic value equal to the difference between the two wing widths. If you make the near wing wider than the far wing, that residual value is positive, so the upside flattens out in profit and there is no risk if price runs away in that direction. All the loss is then concentrated on the other side, where the payoff dips below zero before flattening. This calculator works out that residual value for you, tells you which side carries the risk, and caps the maximum loss so you can size the trade to it.
Should I open a broken-wing butterfly for a credit or a debit? Both are valid and this calculator handles either — enter a positive number for a debit you pay or a negative number for a credit you receive. A credit broken-wing butterfly is the more popular version because it pays you to put the trade on: if price stays on the safe side you simply keep the credit, and the middle strike is where you make the most. The trade-off is that the capped loss on the risk side is larger than the credit, so it is not free money — it is a bet that price will not blow through your skipped wing. A debit version behaves more like a leveraged directional butterfly: you pay a small amount, the risk side loses only that debit, and the safe side still finishes in profit thanks to the residual value. The right choice depends on whether you want income with a defined tail risk (credit) or a cheap directional pin bet with a small fixed cost (debit).
What is the probability a broken-wing butterfly finishes in profit? The probability of profit is the chance that price at expiry lands inside the profit region, which for a broken-wing butterfly is usually a wide zone that runs off to one side. Because one side is safe all the way to infinity, the profit region is often a long tail plus the middle band — much larger than a symmetric butterfly's narrow tent. This calculator estimates the probability from a lognormal move: it takes your annualised volatility and days to expiry to size the one-standard-deviation range, then measures how much of that distribution falls in the profit region. A credit broken-wing butterfly with a safe downside might show a 60-70% chance of finishing in profit, because you only lose if price rallies through your skipped wing. Read that probability next to the maximum loss — a high chance of a small win against a low chance of a larger capped loss is the exact trade-off a broken-wing butterfly is built around.