Long Butterfly

A long call butterfly purchases one call at a lower strike, sells two calls at a middle strike, and purchases one call at a higher strike. The options share an underlying, expiration, and contract size, with equal spacing between strikes. This one-to-two-to-one construction normally opens for a debit and has its greatest expiration profit at the middle strike.

The purchased outer calls limit the loss on either side. Unlike a long straddle, which benefits from a sufficiently large movement away from a strike, the long butterfly has a concentrated expiration profit region and loses its debit outside the outer strikes.

Construction and example

A hypothetical example uses SPY at $750 and calls with 45 days remaining. One complete butterfly uses the following standard 100-share contracts:

The purchased calls cost $42.50 per share in total, while selling the two middle calls brings in $37. The difference is a $5.50 per-share debit, or $550 for the complete position. The $4,250 paid for the outer calls is partly offset by $3,700 received for the middle calls. Although the position contains four contracts, it has three distinct option legs because the middle leg consists of two identical calls.

Expiration payoff

At $725 or below at expiration, all calls have zero payoff and the $550 debit is lost. Between $725 and $750, only the lower call has intrinsic value. Each $1 rise adds $100 to the position’s payoff, first recovering the debit at $730.50 and then increasing profit.

At $750, the lower call has a $25 per-share payoff and all other calls have zero payoff. The $2,500 combined payoff, less the $550 debit, produces the maximum profit of $1,950, or $19.50 per share.

Above $750, the two short calls’ combined obligation grows by $200 for every $1 rise, while the lower purchased call gains $100. The net payoff declines, reaching the second break-even at $769.50. At $775 and above, both purchased calls together gain at the same rate as the two short calls. Equal strike spacing makes their combined payoff zero, leaving the $550 debit loss.

The same one-to-two-to-one construction can use puts at these equally spaced strikes. It produces the same triangular combined expiration payoff before premiums, although the actual entry debit determines profit or loss. Unequal strike spacing creates a broken-wing butterfly whose outer-region value must be calculated separately.

Value before expiration

Near the middle strike, the short calls retain time value, so the amount obtainable by closing the butterfly can be below its maximum expiration payoff. If SPY remains near $750 as expiration approaches, the position tends toward its payoff peak. If it remains beyond either outer strike, the position instead tends toward the debit loss.

Lower implied volatility often benefits the position near its middle strike by reducing the value of possible movements away from the profitable region. Away from the center, that effect can reverse. The three strikes can also have different IVs and respond differently to changes in market expectations. Neither the time effect nor the volatility effect has a uniform sign throughout the underlying-price range.

Closing sells the two purchased outer calls and repurchases the two middle calls. The signed net proceeds must exceed $5.50 per share to produce a profit. The full one-to-two-to-one ratio is relevant: closing only part of a leg changes the remaining exposure and can remove the original loss limit.

Exercise, assignment, and execution

SPY calls permit early exercise. Either or both of the two short $750 calls can be assigned, producing a sale of 100 or 200 shares respectively. The purchased calls remain separate rights that can be sold or exercised according to their own terms. The account must support any interim shares or delivery requirements.

Near the middle strike at expiration, the lower purchased call may be exercised while assignment of the middle calls remains uncertain. A share position can therefore remain even when the calculated butterfly profit is near its maximum. The options do not exercise as a single package, and subsequent share-price changes lie outside the completed expiration payoff calculation.

A complex order can trade the option legs at a net price while maintaining their ratio for each completed package. Selling options and trading any resulting shares may recover time value that would be surrendered through exercise, subject to the prices and quantities available.

Payoff formulas

Let $K_L<K_M<K_H$ be the three strikes and let their equal spacing be $w=K_M-K_L=K_H-K_M$. With debit per share $d$, final underlying price $S_T$, multiplier $M$, and $q$ complete butterflies:

The purchased-call payoffs are added and twice the middle-call payoff is subtracted. For $0<d<w$:

Maximum profit occurs at $K_M$, where the combined payoff equals one wing’s width. Both roots lie inside the outer strikes. At or beyond either outer strike, the combined option payoff is zero and the full debit is lost. Quantity scales the dollar results only when complete one-to-two-to-one positions are repeated.