Butterfly (options)

In finance, a butterfly (or simply fly) is a limited risk, non-directional options strategy that is designed to have a high probability of earning a limited profit when the future volatility of the underlying asset is expected to be lower (when long the butterfly) or higher (when short the butterfly) than that asset's current implied volatility. 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). 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. In the United States, margin requirements for all options positions, including a butterfly, are governed by what is known as Regulation T. However brokers are permitted to apply more stringent margin requirements than the regulations. The price of a butterfly centered around some strike price can be used to estimate the implied probability of the underlying being at that strike price at expiry.