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Encyclopedia > Butterfly (options)

In options trading, a butterfly is a combination trade resulting in the following net position: In finance, an option is a contract whereby the contract buyer has a right to exercise a feature of the contract (the option) at future date (the exercise date), and the writer (seller) has the obligation to honour the specified feature of the contract. ... In finance, a postion may be: A commitment to buy or sell a given amount of securities or commodities; The amount of securities or commodities held by a person, firm, or institution; or The ownership status of a persons or institutions investments. ...

  • 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. In finance, a long position in a security, such as a stock or a bond, or equivalently to be long a security, means the holder of the position owns the security. ... It has been suggested that this article or section be merged with Short selling. ... For an option contract, expiration is the date on which the contract expires. ...


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:

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

and this is equivalent to the call version (as can be verified via Put-call_parity). In financial mathematics, put-call parity defines a relationship between the price of a European call option and a European put option - both with the identical strike price and expiry. ...


The double position in the middle is called the body, while the two other positions are called the wings.


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

  Financial derivatives  
Options
Vanilla Types: Option styles |Call | Put | Warrants | Fixed income | Employee stock option | FX
Strategies: Covered calls | Naked puts | Bear Call Spread | Bear Put Spread | Bull Call Spread | Bull Put Spread | Calendar spread | Straddle | Long Straddle | Long Strangle | Butterfly | Short Butterfly Spread | Short Straddle | Short Strangle | Vertical spread | Volatility arbitrage | Debit Spread | Credit spread | Synthetic
Exotics: Asian | Lookbacks | Barrier | Binary | Swaptions | Mountain range
Valuation: Moneyness | Option time value | Black-Scholes | Black | Binomial | Stochastic volatility | Implied volatility
Swaps
Interest rate | Total return | Equity | Credit default | Forex | Cross-currency | Constant maturity | Basis | Variance


 

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