Comparing Butterfly and Iron Butterfly Expiration Payoffs

Summary

The document presents a question about the relationship between a long call butterfly and a short iron butterfly. It gives a four-option position consisting of a long lower-strike put, short middle-strike put and call, and long upper-strike call, then compares its expiration value with that of a traditional butterfly when the underlying finishes above the middle strike.

The example shows that the positions do not have identical payoffs in the stated setup: the traditional butterfly is reported as positive while the iron position is negative. The question also asks why the prices of the two structures should add to the strike spacing. However, the document contains no answer or derivation, so it does not resolve the apparent contradiction or establish the price relationship. It is useful as a prompt for examining payoff diagrams and option parity, but readers need additional explanation to determine how premiums, payoff conventions, and position definitions fit together.

Key ideas

• The document compares a traditional long butterfly with a four-leg iron position using the same strike levels.
• It reports different expiration values for the two positions at an underlying price above the middle strike.
• The question raises a proposed relationship between butterfly prices and the spacing between strikes.
• No explanation or derivation is provided, so the payoff comparison remains unresolved.

Tags

# Iron Butterfly Relationship with Butterfly


# Iron Butterfly Relationship with Butterfly












I'm reading Natenburg's Options book, and I'm not understanding why "Buying a traditional butterfly is equivalent to selling an iron butterfly," because later in the text Natenburg says that "If we sell the June 95 / 100 / 105 iron butterfly we will take in some amount between zero and 5.00. We also hope that the underlying will finish at 100, in which case all the options will be worthless and we will profit by the amount of the original sale," but if selling/shorting the iron butterfly is longing the original butterfly, why don't we have the same payoff?

And why must the prices of a butterfly and iron butterfly must add up to the difference in exercise prices?

Could someone explain and clarify the reasoning? Thanks!

Like the book uses the example of the following position:

+1 June 95 put

−1 June 100 call

−1 June 100 put

+1 June 105 call

and compares it with a usual long 95/100/105 butterfly. At expiration, if the underlying is worth $102, the butterfly is worth \$3, but the position given (the short iron butterfly) is worth -\$2.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.