Butterfly spread is a "classic" options strategy, which combines the simultaneous purchase and sale of three options with three different strikes.

Options, beyond being very interesting individual instruments, when combined, allow for extremely successful strategies. Among these strategies, the butterfly occupies a prime position.

**Characteristics of butterfly spread**

Butterfly is a strategy that combines the purchase and sale of 3 options of the same type (either calls or puts) with the following characteristics:

▪ These options have the same expiry date

▪ These options relate to the same underlying asset

▪ The strike prices, the "strikes", are spaced from each other in such a way that: if we call K1, K2 and K3 the strikes of these options, the difference between K1 and K2 is identical to the difference between K2 and K3. In other words, the strikes K1 and K3 are equidistant from K2.

Example:

K1 = 90, K2 = 100, K3 = 110 and

K2 – K1 = K3 – K2 = 10

or again, K1 = 26, K2 = 28, K3 = 30 and

K2 – K1 = K3 – K2 = 2

**Strategy**

Butterfly consists of:

- The purchase of one K1 strike option

- The sale of two K2 strike options

- The purchase of one K3 strike option

The butterfly spread can be built with calls or puts.

For example, you can use the following example:

Call butterfly spread on the XYZ share:

- The purchase of 1 Call with strike 85 expiring in December 2021.

- The sale of 2 Calls with strike 105 expiring in December 2021

- The purchase of 1 Call with strike 125 expiring in December 2021

Put butterfly on XYZ stock

- The purchase of 1 Put with strike 85 expiring in December 2021

- The sale of 2 Puts with strike 105 expiring December 2021

- The purchase of 1 Put with strike 125 expiring in December 2021

By the call-put parity relationship the two butterflies are identical in risk profile and payoffs.

**Graphical representation**

A call butterfly 46/50/54, maturing 1 year.

It's a 2D representation of the payoff of a butterfly

**Advantage of this strategy**

The advantage is obvious on the graph. For a low initial investment, the prospect of gains and losses is very high around the sold strike. The farther away from the sold strike, on either side, the gain gradually fades away, until the maximum loss is equal to the price of the butterfly.

This means that for a given objective, a given term, one can easily maximize a gain by buying a butterfly spread.

**Risk**

The risk is limited to the amount of the purchase of the butterfly when trading in European type options, exercisable at maturity.

**Credit**

It costs money to construct a long butterfly spread.

We therefore say that we buy a butterfly, when we buy one K1 strike option (call or put), sell two K2 strike options and buy one K3 strike option, with K1 < K2 < K2 and K2 – K1 = K3 – K2.

So we say that we are selling a butterfly spread, when we sell a K1 strike option (call or put), buy two K2 strike options and sell a K3 strike option, where K1 < K2 < K3 and K2 – K1 = K3 – K2