How to use the butterfly spread calculator
A long butterfly uses three strikes and four options of the same type and expiry: buy one at the lower strike, sell two at the middle strike and buy one at the upper strike. It is a low-cost bet that the price will finish near the middle strike.
- Choose a call or put butterfly. The labels change to match.
- Choose how to enter the premiums: each leg’s quote, or the net debit your broker shows for the whole order.
- Enter the current price and the number of butterflies. One butterfly is 1 + 2 + 1 contracts, each on 100 shares.
- Enter the three strikes, lowest first. Equal distances between them make a standard butterfly; unequal distances make a broken-wing butterfly, and the calculator warns you.
- Enter the premiums per share. The middle premium is for one option; the calculator doubles it.
The chart shows the tent-shaped payoff at expiry with the break-evens and the current price marked, and the table gives the result at each strike and break-even.
The formulas
Maximum profit = (Middle strike − Lower strike − Net debit) × 100 × Contracts
Maximum loss = Net debit × 100 × Contracts
Lower break-even = Lower strike + Net debit
Upper break-even = Upper strike − Net debitThese are the formulas for a long call butterfly with equal wings; a put butterfly with equal wings gives the same results. For a broken-wing butterfly, the calculator finds the maximum profit, maximum loss and break-evens directly from the payoff at every strike. Return on risk = Maximum profit ÷ Maximum loss.
A worked example
A stock trades at $100 and you expect it to be close to that price at expiry. You buy the $95 call for $6.20, sell two $100 calls for $2.95 each and buy the $105 call for $1.
The net debit is $1.30 per share, so 2 contracts cost $260.00. That is also the maximum loss, if the stock ends below $95 or above $105.
If the stock closes exactly at $100, the lower call is worth $5, the others expire worthless, and the maximum profit is $740.00. The break-evens are $96.30 and $103.70, so the profit zone is $7.40 wide.
The return on risk is 284.62%: you risk $0.35 for each dollar of maximum profit.
The same strikes with puts and the same $1.30 debit give an identical result: a maximum profit of $740.00 and break-evens of $96.30 and $103.70.
How wing width changes the trade
Wider wings cost more but give a wider profit zone. The three butterflies below are centered on $100; the debits are illustrative.
| Strikes | Net debit | Max profit (2 contracts) | Max loss | Return on risk | Break-evens |
|---|---|---|---|---|---|
| $97.50 / $100 / $102.50 | $0.45 | $410.00 | $90.00 | 455.56% | $97.95 and $102.05 |
| $95 / $100 / $105 | $1.30 | $740.00 | $260.00 | 284.62% | $96.30 and $103.70 |
| $90 / $100 / $110 | $3.40 | $1,320.00 | $680.00 | 194.12% | $93.40 and $106.60 |
The narrow butterfly has the best return on risk on paper, but its profit zone is only $4.10 wide. The wide one is far more forgiving, with a $13.20 zone, at the cost of a bigger debit. The high return on risk of any butterfly is paid for with a small chance of landing near the peak: the maximum profit is earned at one price only.
Targeting a price away from today’s
The middle strike does not have to be at the current price. A butterfly centered above or below the price is a cheap way to express a view on where the stock will be at expiry. Centering on $105 with the stock at $100, for a $0.95 debit, risks $190.00 to make up to $810.00, with break-evens at $100.95 and $109.05. If the stock stays at $100, the whole debit is lost.
Broken-wing butterflies
Moving one long strike further out lowers the cost. With strikes of $95, $100 and $110 the position can even be opened for a credit, here $20.00. If the stock falls below $95, you keep that credit; at $100 the profit peaks at $520.00; above $110 the loss is $480.00, because the upper wing is twice as wide as the lower one. There is only one break-even, at $105.20. A broken-wing butterfly trades risk on one side for none on the other, and is only sensible if you are comfortable with the price moving against the wide wing.
What this calculator does not include
- The path before expiry. A butterfly’s value changes slowly at first; most of the payoff shown appears in the final days. Time decay and volatility, shown by the option Greeks calculator, drive its value until then.
- Commissions and the bid-ask spread. Four contracts per butterfly make costs a large share of a small debit, so use real fill prices.
- Early assignment. American-style stock options can be assigned early, especially in-the-money short calls before a dividend. An assignment leaves a stock position until the rest of the spread is closed.
- Settlement risk. If the price closes near a short strike at expiry, you may not know until after the close whether you will be assigned.
- Probabilities. The calculator shows the result at each price, not how likely each price is.