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In
finance Finance is the study and discipline of money, currency and capital assets. It is related to, but not synonymous with economics, the study of production, distribution, and consumption of money, assets, goods and services (the discipline of f ...
, a butterfly (or simply fly) is a limited risk, non-directional
options strategy Option strategies are the simultaneous, and often mixed, buying or selling of one or more options that differ in one or more of the options' variables. Call options, simply known as Calls, give the buyer a right to buy a particular stock at that ...
that is designed to have a high
probability Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1, where, roughly speaking, ...
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 In financial mathematics, the implied volatility (IV) of an option contract is that value of the volatility of the underlying instrument which, when input in an option pricing model (such as Black–Scholes), will return a theoretical value equ ...
.


Long butterfly

A
long Long may refer to: Measurement * Long, characteristic of something of great duration * Long, characteristic of something of great length * Longitude (abbreviation: long.), a geographic coordinate * Longa (music), note value in early music mensu ...
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 Option or Options may refer to: Computing *Option key, a key on Apple computer keyboards *Option type, a polymorphic data type in programming languages *Command-line option, an optional parameter to a command *OPTIONS, an HTTP request method ...
: *
Long Long may refer to: Measurement * Long, characteristic of something of great duration * Long, characteristic of something of great length * Longitude (abbreviation: long.), a geographic coordinate * Longa (music), note value in early music mensu ...
1
call Call or Calls may refer to: Arts, entertainment, and media Games * Call, a type of betting in poker * Call, in the game of contract bridge, a bid, pass, double, or redouble in the bidding stage Music and dance * Call (band), from Lahore, Paki ...
with a
strike price In finance, the strike price (or exercise price) of an option is a fixed price at which the owner of the option can buy (in the case of a call), or sell (in the case of a put), the underlying security or commodity. The strike price may be set ...
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 In financial mathematics, put–call parity defines a relationship between the price of a European call option and European put option, both with the identical strike price and expiry, namely that a portfolio of a long call option and a short pu ...
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.


Margin requirements

In the United States, margin requirements for all options positions, including a butterfly, are governed by what is known as
Regulation T Federal Reserve Board Regulation T (also referred to as Reg T) is 12 CFR §220 – Code of Federal Regulations, Title 12, Chapter II, Subchapter A, Part 220 (Credit by Brokers and Dealers). Regulation T governs the extension of credit by securiti ...
. However brokers are permitted to apply more stringent margin requirements than the regulations.


Use in calculating implied distributions

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. This means the set of market prices for butterflies centered around different strike prices can be used to infer the market's belief about the probability distribution for the underlying price at expiry. This implied distribution may be different from the lognormal distribution assumed in the popular Black-Scholes model, and studying it can reveal ways in which real-world assets differ from the idealized assets described by Black-Scholes.


Butterfly variations

#The double option position in the middle is called the body, while the two other positions are called the wings. #In case the distance between middle strike price and strikes above and below is unequal, such position is referred to as "broken wings" butterfly (or "broken fly" for short). # An
iron butterfly Iron Butterfly is an American rock band formed in San Diego, California, in 1966. They are best known for the 1968 hit " In-A-Gadda-Da-Vida", providing a dramatic sound that led the way towards the development of hard rock and heavy metal musi ...
recreates the payoff diagram of a butterfly, but with a combination of two calls and two puts. # The option strategy where the middle options (the body) have different strike prices is known as a
Condor Condor is the common name for two species of New World vultures, each in a monotypic genus. The name derives from the Quechua ''kuntur''. They are the largest flying land birds in the Western Hemisphere. They are: * The Andean condor (''Vu ...
. # A Christmas tree butterfly (not to be confused with the unrelated option combination also called a Christmas tree) consists of six options used to create a payoff diagram similar to a butterfly but slightly bearish or bullish instead of directionally neutral.


References

* * {{Derivatives market Options (finance)