Model and input conventions
Add the intrinsic payoff of the lower call and upper call, then subtract twice the middle call’s intrinsic payoff. Premium paid is lower premium plus upper premium minus twice the premium received for each middle call. Quantity scales a complete one-to-two-to-one package in underlying units. Equal spacing makes the gross payoff zero outside the outer strikes and gives its maximum at the middle strike.
Worked numerical example
Using strikes of 90, 100 and 110, premiums of 12 for the lower call, 7 for each middle call and 4 for the upper call create a debit of 2. With one package and no fees, the worst expiry P&L is −2 and the best is +8 at 100. Break-even prices are 92 and 108. A terminal price of 110 or above again loses the original 2 debit.
Read the scenario table
The table includes every strike and valid zero-P&L boundary. Review the middle strike explicitly: the maximum does not occur simply because the underlying stays anywhere between the outer wings. Compare rows approaching the center from both directions to see the opposite payoff slopes. The quantity input already includes the package multiplier, while the middle-call premium field remains a per-call, per-underlying-unit quote.
Where the model stops
This model excludes asymmetric or broken-wing butterflies by rejecting unequal spacing. It also excludes interim option time value, assignment, premium financing and separate execution of the two short calls. Terminal bounded loss does not reproduce a venue’s margin process. A higher debit can eliminate the profitable region completely, so the calculator derives boundaries from the actual entered cash flows rather than presuming standard example economics.