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In options trading, a butterfly (to be precise a long butterfly) is a combination trade resulting in the following net position:

• Long 1 call at (X − a) strike
• Short 2 calls at X strike
• Long 1 call at (X + a) strike

all with the same expiration date. At expiration the position will be worth zero if the underlying is below X−a or above X+a, and will be worth a positive amount between these two values. The payoff function is shaped like an upside-down V, and the maximum payoff occurs at X.

Since the payoff is sometimes zero, sometimes positive, the price of a butterfly is always non-negative (to avoid an arbitrage opportunity).

A butterfly can also be created as follows:

• Long 1 put at (X − a) strike
• Short 2 puts at X strike
• Long 1 put at (X + a) strike

and this is equivalent to the call version (as can be verified via put–call parity).

The double position in the middle is called the body, while the two other positions are called the wings. A related strategy where the middle two positions have differing strike values is known as an Iron condor.

In an unbalanced butterfly the variable a can have 2 different values.

The butterfly spread is a neutral options trading strategy that is a combination of a bull spread and a bear spread. It is a limited profit, limited risk options strategy. There are 3 striking prices involved in a butterfly spread and it can be constructed using calls or puts.

Long butterflies are entered when the investor thinks that the underlying stock will not rise or fall much by expiration (i.e. when the investor is bearish on volatility). Using calls, the long butterfly can be constructed by buying one lower striking in-the-money call, writing two at-the-money calls and buying another higher striking out-of-the-money call. A resulting net debit is taken to enter the trade, hence it is also a debit spread.

A long butterfly spread can also be constructed using puts and is known as a long put butterfly.

Short butterfly is the name of a neutral-outlook, options trading strategy that involves trading options at three different strike prices. The short butterfly is a neutral strategy like the long butterfly spread but bullish on volatility. It is a limited profit, limited risk options trading strategy and it can be constructed using calls or puts.

Using calls, the short butterfly can be constructed by writing one lower striking call, buying two at-the-money calls and writing another higher striking call. A net credit is received upon entering this spread. Hence, the short butterfly is also a credit spread.

• McMillan, Lawrence G. (2002). Options as a Strategic Investment, 4th ed., New York : New York Institute of Finance. ISBN 0-7352-0197-8.