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Butterfly (options)

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Title: Butterfly (options)  
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Butterfly (options)

Payoff chart from buying a butterfly spread.
Profit from a long butterfly spread position. The spread is created by buying a call with a relatively low strike (x1), buying a call with a relatively high strike (x3), and shorting two calls with a strike in between (x2).

In finance, a butterfly is a limited risk, non-directional options strategy that is designed to have a large probability of earning a limited profit when the future volatility of the underlying asset is expected to be lower than the implied volatility.

Long butterfly

A long butterfly position will make profit if the future volatility is lower than the implied volatility.

A long butterfly options strategy consists of the following options:

  • Long 1 call with a strike price of (X − a)
  • Short 2 calls with a strike price of X
  • Long 1 call with a strike price of (X + a)

where X = the spot price (i.e. current market price of underlying) and a > 0.

Using put–call parity a long butterfly can also be created as follows:

  • Long 1 put with a strike price of (X + a)
  • Short 2 puts with a strike price of X
  • Long 1 put with a strike price of (X − a)

where X = the spot price and a > 0.

All the options have the same expiration date.

At expiration the value (but not the profit) of the butterfly will be:

  • zero if the price of the underlying is below (X − a) or above (X + a)
  • positive if the price of the underlying is between (X - a) and (X + a)

The maximum value occurs at X (see diagram).

Short butterfly

A short butterfly position will make profit if the future volatility is higher than the implied volatility.

A short butterfly options strategy consists of the same options as a long butterfly. However now the middle strike option position is a long position and the upper and lower strike option positions are short.

Butterfly P/L graph

Since the butterfly options strategy is a complex one and contains 3 "legs" (options with 3 different strike), its P/L graph is quite complicated and changes considerably as time moves forward to the expiration.

This is a graph showing the P/L (profit / loss) for a 1-year butterfly options strategy 5 days before expiry:

[[File:Butterfly

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