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.