Butterfly Spreads

The butterfly spread: 

- is a neutral vanilla option-trading strategy.

- is a combination of a bull spread and a bear spread with same maturity. 

- offers a limited profit at a limited risk. 

- involves 3 strikes and can be constructed using calls or puts. 

- can be bought by an investor who believes that asset will not move by much in either direction by expiry of options. 

- enables the holder to capture the curvature of the implied volatility skew.​

- is short volatility. 

 

Using call options, a butterfly spread constitutes: 

- long 1 lower ITM call 

- short 2 ATM calls 

- long 1 higher OTM call 

 

Using put options, a butterfly spread constitutes: 

- long 1 lower OTM put 

- short 2 ATM puts

- long 1 higher ITM put

 

Butterfly spread

 

One buying this butterfly spread receives a positive payoff and pays an initial investment equal to:

 

Profit/Loss = 

 

Limited Profit:

Max Profit = 

The maximum payoff occurs when ST = K and is equal to ε.

 

Limited Loss:

Max loss = premium paid + commissions paid

 

Break-even points:

There are 2 break-even points for the butterfly spread position.

  • Upper Breakeven Point = Strike Price of Higher Strike Long Call/Put - Net Premium Paid
  • Lower Breakeven Point = Strike Price of Lower Strike Long Call/Put + Net Premium Paid

 

Commissions:

Commission charges can make a significant impact to overall profit or loss when implementing option spreads strategies.

Their effect is even more pronounced for the butterfly spread as there are 4 legs involved in this trade. 

 

Note that a butterfly spread can also be seen as: 

- long a strangle: long put with lower OTM strike / long call with higher OTM strike

- short a straddle: short ATM call / short ATM put

 

Butterflies are one of the three main products quoted in a vanilla FX option market. 

The other two being ATM straddles and risk reversals. 

 

Brokers will quote butterflies as the vol difference between the strangle and straddle vol. 

Quants will use this vol when constructing the vol surface. 

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