# Butterfly (options)

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In finance, a butterfly 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 or higher than the implied volatility when long or short respectively.

Finance is a field that is concerned with the allocation (investment) of assets and liabilities over space and time, often under conditions of risk or uncertainty. Finance can also be defined as the art of money management. Participants in the market aim to price assets based on their risk level, fundamental value, and their expected rate of return. Finance can be split into three sub-categories: public finance, corporate finance and personal finance.

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 option's strike price. Conversely, put options, simply known as puts, give the buyer the right to sell a particular stock at the option's strike price. This is often done to gain exposure to a specific type of opportunity or risk while eliminating other risks as part of a trading strategy. A very straightforward strategy might simply be the buying or selling of a single option, however option strategies often refer to a combination of simultaneous buying and or selling of options.

Probability is the measure of the likelihood that an event will occur. See glossary of probability and statistics. Probability quantifies as a number between 0 and 1, where, loosely speaking, 0 indicates impossibility and 1 indicates certainty. The higher the probability of an event, the more likely it is that the event will occur. A simple example is the tossing of a fair (unbiased) coin. Since the coin is fair, the two outcomes are both equally probable; the probability of "heads" equals the probability of "tails"; and since no other outcomes are possible, the probability of either "heads" or "tails" is 1/2.

## Long butterfly

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

In finance, a short sale is the sale of an asset that the seller has borrowed in order to profit from a subsequent fall in the price of the asset. After borrowing the asset, the short seller sells it to a buyer at the market price at that time. Subsequently, the resulting short position is "covered" when the seller repurchases the same asset in a market transaction and delivers the purchased asset back to the lender to replace the asset that was initially borrowed. In the event of an interim price decline, the short seller will profit, since the cost of (re)purchase will be less than the proceeds received upon the initial (short) sale. Conversely, the short position will result in a loss if the price of a shorted asset rises prior to repurchase.

A long butterfly options strategy consists of the following options:

In finance, an option is a contract which gives the buyer the right, but not the obligation, to buy or sell an underlying asset or instrument at a specified strike price prior to or on a specified date, depending on the form of the option. The strike price may be set by reference to the spot price of the underlying security or commodity on the day an option is taken out, or it may be fixed at a discount or at a premium. The seller has the corresponding obligation to fulfill the transaction – to sell or buy – if the buyer (owner) "exercises" the option. An option that conveys to the owner the right to buy at a specific price is referred to as a call; an option that conveys the right of the owner to sell at a specific price is referred to as a put. Both are commonly traded, but the call option is more frequently discussed.

• 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)

In finance, a long position in a financial instrument, means the holder of the position owns a positive amount of the instrument. It is contrasted with going short.

A call option, often simply labeled a "call", is a financial contract between two parties, the buyer and the seller of this type of option. The buyer of the call option has the right, but not the obligation, to buy an agreed quantity of a particular commodity or financial instrument from the seller of the option at a certain time for a certain price. The seller is obligated to selling the commodity or financial instrument to the buyer if the buyer so decides. The buyer pays a fee for this right. The term "call" comes from the fact that the owner has the right to "call the stock away" from the seller.

In finance, the strike price of an option is the fixed price at which the owner of the option can buy, or sell, the underlying security or commodity. The strike price may be set by reference to the spot price of the underlying security or commodity on the day an option is taken out, or it may be fixed at a discount or at a premium.

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:

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 put option is equivalent to a single forward contract at this strike price and expiry. This is because if the price at expiry is above the strike price, the call will be exercised, while if it is below, the put will be exercised, and thus in either case one unit of the asset will be purchased for the strike price, exactly as in a forward contract.

• 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:

## Margin Requirements

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.

## Butterfly Variations

1. The double option position in the middle is called the body, while the two other positions are called the wings.
2. The option strategy where the middle options (the body) have different strike prices is known as a Condor.
3. In case the distance between middle strike price and strikes above and below is unequal, such position is referred to as "broken wings" butterfly.

## Related Research Articles

In finance, a put or put option is a stock market device which gives the owner the right, but not the obligation, to sell an asset, at a specified price, by a predetermined date to a given party. The purchase of a put option is interpreted as a negative sentiment about the future value of the underlying stock. The term "put" comes from the fact that the owner has the right to "put up for sale" the stock or index.

In finance, a straddle strategy refers to two transactions that share the same security, with positions that offset one another. One holds long risk, the other short. As a result, it involves the purchase or sale of particular option derivatives that allow the holder to profit based on how much the price of the underlying security moves, regardless of the direction of price movement.

In finance, the time value (TV) of an option is the premium a rational investor would pay over its current exercise value, based on the probability it will increase in value before expiry. For an American option this value is always greater than zero in a fair market, thus an option is always worth more than its current exercise value.. As an option can be thought of as 'price insurance', TV can be thought of as the risk premium the option seller charges the buyer—the higher the expected risk, the higher the premium. Conversely, TV can be thought of as the price an investor is willing to pay for potential upside.

Volatility smiles are implied volatility patterns that arise in pricing financial options. It corresponds to finding one single parameter that is needed to be modified for the Black-Scholes formula to fit market prices. In particular for a given expiration, options whose strike price differs substantially from the underlying asset's price command higher prices than what is suggested by standard option pricing models. These options are said to be either deep in-the-money or out-of-the-money.

In finance, risk reversal can refer to a measure of the volatility skew or to an investment strategy.

In options trading, a box spread is a combination of positions that has a certain payoff, considered to be simply "delta neutral interest rate position". For example, a bull spread constructed from calls combined with a bear spread constructed from puts has a constant payoff of the difference in exercise prices assuming that the underlying stock does not go ex-dividend before the expiration of the options. If the underlying asset has a dividend of x, then the settled value of the box will be 10+x. Under the no-arbitrage assumption, the net premium paid out to acquire this position should be equal to the present value of the payoff.

In finance, a calendar spread is a spread trade involving the simultaneous purchase of futures or options expiring on a particular date and the sale of the same instrument expiring on another date. The legs of the spread vary only in expiration date; they are based on the same underlying market and strike price.

The iron condor is an option trading strategy utilizing two vertical spreads – a put spread and a call spread with the same expiration and four different strikes. A long iron condor is essentially selling both sides of the underlying instrument by simultaneously shorting the same number of calls and puts, then covering each position with the purchase of further out of the money call(s) and put(s) respectively. The converse produces a short iron condor.

In finance an iron butterfly, also known as the ironfly, is the name of an advanced, neutral-outlook, options trading strategy that involves buying and holding four different options at three different strike prices. It is a limited-risk, limited-profit trading strategy that is structured for a larger probability of earning smaller limited profit when the underlying stock is perceived to have a low volatility.

Options spreads are the basic building blocks of many options trading strategies. A spread position is entered by buying and selling equal number of options of the same class on the same underlying security but with different strike prices or expiration dates.

A Ratio spread is a complex, multileg options position that is a variation of a vertical spread. Like a vertical, the ratio spread involves buying and selling options on the same underlying security with different strike prices and the same expiration date. Unlike a vertical spread, a number of option contracts sold is not equal to a number of contracts bought. An unequal number of options contracts gives this spread certain unique properties compared to a regular vertical spread. A typical ratio spread would be where twice as many option contracts are sold, thus forming a 1:2 ratio.

The backspread is the converse strategy to the ratio spread and is also known as reverse ratio spread. Using calls, a bullish strategy known as the call backspread can be constructed and with puts, a strategy known as the put backspread can be constructed.

Options arbitrage trades are commonly performed in the options market to earn small profits with very little or zero risk.

In finance, a credit spread, or net credit spread is an options strategy that involves a purchase of one option and a sale of another option in the same class and expiration but different strike prices. It is designed to make a profit when the spreads between the two options narrows.

In finance, a strangle is an investment strategy involving the purchase or sale of particular option derivatives that allows the holder to profit based on how much the price of the underlying security moves, with relatively minimal exposure to the direction of price movement. A purchase of particular options is known as a long strangle, while a sale of the same options is known as a short strangle. As an options position strangle is a variation of a more generic straddle position. Strangle's key difference from a straddle is in giving investor choice of balancing cost of opening a strangle versus a probability of profit. For example, given the same underlying security, strangle positions can be constructed with low cost and low probability of profit. Low cost is relative and comparable to a cost of straddle on the same underlying. Strangles can be used with equity options, index options or options on futures.

Stock option return calculations provide investors an easy metric for comparing stock option positions. For example, for two stock option positions which appear identical, the potential stock option return may be useful for determining which position has the highest relative potential return.

In options trading, a jade lizard is a custom option strategy which consists of a bear vertical spread created using call options, with the addition of a put option sold at a strike price lower than the strike prices of the call spread. For one underlying security, same expiration date, this strategy consists of buying a call option at one strike price, selling another call option at a lower strike price, then selling an OTM put option at a strike price lower than that of both call options. The addition of the sale of a put option is consistent with the expected move of the underlying and results in additional premium collected. The jade lizard strategy takes advantage of the volatility skew inherently priced into options with naked puts trading richer in premium than naked calls and short call spreads trading richer in premium than short put spreads. This volatility skew effect allows the trader to collect more premium for the overall position and thus, increasing the position's probability of profit. The term "jade lizard" was first used by former CBOE floor traders, Liz Dierking and Jenny Andrews, on the Liz & Jny Show on the Tastytrade Network.