A butterfly is an option spread position involving two vertical spreads, one long and one short, in which the short strike is common.

The butterfly spread therefore involves three equidistant strikes.  For a long butterfly, a net debit is paid.  In this strategy, the trader is long one contract at a lower strike (wing), short two contracts at a middle strike (the body), and long one contract at an upper strike (wing), each with the same expiration.  The size may be increased, although the same 1-2-1 relationship remains the same where the “body” is 2x the size of each “wing” (ex: 2-4-2, 3-6-3, 4-8-4, etc.).

Directional Butterflies

Butterflies can be done using calls or puts, and can be constructed as either a bullish, bearish, or neutral position.

A neutral butterfly would use an ATM short strike, expecting price to stay at or near current levels by expiration.  The neutral butterfly is therefore fully dependent upon theta decay of the short options.

A bullish butterfly would use an OTM call as the short strike.  This way, an increase in the share price would bring it closer to the short strike, which is where max gain would be seen at expiration.

A bearish butterfly would use an OTM put as the short strike.  With this position, a decrease in the share price would bring it closer to the short strike where the max gain would be seen at expiration.

Construction of a Butterfly Spread

A butterfly spread is a long vertical spread overlapping the short strike with a short vertical spread.  In the case of a bullish call butterfly, the individual trade components are:

Long 1 $50 call (long component of a long call vertical)
Short 1 $55 call (short component of a long call vertical)
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Short 1 $55 call (short component of a short call vertical)
Long 1 $60 call (long component of a short call vertical)

Because the short strikes overlap from each vertical spread, the net butterfly position is:

Long 1 $50 call (wing)
Short 2 $55 calls (body)
Long 1 $60 call (wing)

Probability

Butterfly spreads are low-probability, high-reward positions.  This means the probability of success is low, but they can produce big profits when they work.  The probability of success for a butterfly is calculated by dividing the debit paid by the width of the strikes.

For example, take a $50/$55/$60 call butterfly done for a debit of $0.60.  To determine the probability of the trade, we take the $0.60 debit divided by the $5 strike width ($0.60 / $5.00 = .12), which gives the trade a 12% probability of success.

The max gain for a butterfly is the difference between one wing strike and the body strike (upper vertical spread or lower vertical spread) less the debit paid.  Using the same $50/$55/$60 example, it’s a $5 wide butterfly which cost $0.60, which would create a max gain of $4.40 ($5 – $0.60 = $4.40).  It’s often sensible to close out a butterfly position when either the directional bias for the trade has changed, or when most of the profit has been made with little time remaining until expiration.

Other Factors

Because butterflies are so dependent upon theta decay of the short options, they become much more sensitive to movement as expiration approaches.  Some traders like to place butterflies at levels where they expect the stock to “pin” at expiration.  Because they are low-probability trades, position size should be smaller.

Butterflies tend to be somewhat commission intensive due to the multiple legs of the position.  Vega is highest at the money, so a long butterfly is generally considered a vega negative trade.  This means that the trade will benefit from a contraction in IV, particularly when price is near the short strike, as contracting IV suggests a lower likelihood of price moving.  When price is nearer to the outer strikes, it will benefit from an increase in IV (vega positive), as that improves the chances of price moving toward the short strike.

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An iron condor is a neutral strategy pairing an OTM short call vertical spread and an OTM short put vertical spread on the same underlying with the same expiration.

With price expected to stay between the short call and put strikes, the time value erodes and premium on both sides can be collected.  Iron condors are positive theta trades since they benefit from time decay.  Because each vertical spread is sold for a credit, iron condors are sold for credits.  Iron condors benefit from stagnating price, as well as the collapse of implied volatility since they are short vega.  This means that higher implied volatility will result in a greater initial credit when selling an iron condor.

An iron condor is sold for a credit as a defined-risk, defined-profit strategy.  The max profit potential is the premium collected on the sale of the two verticals.  The max loss is the width of either vertical spread less the credit received.  Because price can only move through one of the verticals (either the call side or put side), it limits the max risk to the width of the vertical spread.

The downside breakeven can be calculated by subtracting the total premium collected from the short put strike, whereas the upside breakeven is the total premium collected added to the short call strike.

The farther OTM the short strikes, the less the initial credit an iron condor will collect.  Iron condors will also collect smaller initial credits when the short strikes are farther apart, although wide iron condors will carry a higher probability of success.

The probability of success for an iron condor can be found by dividing the real risk by the width of the spread.  For example, take a $5 wide iron condor which is sold for a $2 credit.  Because $2 is collected up front and the spread itself is only $5 wide, the real risk in the trade is $3 ($5 – $2 = $3).  $3 (real risk) divided by $5 (the width of the spread) gives a 60% probability of success.

Non-Directional Iron Condors

Typically, iron condors are executed with both short strikes equidistant from the current price.  This allows for matching freedom of movement in either direction before either side (short call or short put) would be tested.

Directional/Skewed Iron Condors

A standard iron condor is executed with the short strikes on both the call and put sides being equidistant from the current price.  An example would be an iron condor on a $50 stock where the short call is at $55 and the short put is at $45, both $5 away from the current price.

Iron condors can be entered as directional positions by placing one of the short strikes closer to the money.  By altering the proximity of one of the short strikes to the current price, price is allowed less freedom of movement before that vertical spread would be tested, but now it has more freedom of movement in the other direction before a test of that short strike would occur.

For example, a neutral to bullish iron condor might look something like this:

XYZ trading at $70
Sell the $67.50/65 put vertical
Sell the $77.50/80 call vertical

Both vertical spreads are $2.50 wide, but the put vertical is placed closer to the money ($2.50 away) than the short call vertical ($7.50 away).  This would be a neutral to bullish trade where XYZ is expected to stay between the short strikes ($67.50 to $77.50), but more room is allowed on the upside, giving it a slightly bullish bias.

It’s important to note that even directional iron condors still have defined risk and defined profit.

Unbalanced Iron Condors

A standard iron condor is composed of short call and put vertical spreads which match in size, width, or both.  Unbalancing the iron condor can give it a directional bias.

Strike Width

An unbalanced iron condor will have one vertical spread wider than the other.  For example, an unbalanced iron condor might be the $60/$70/$75/$80 iron condor where the put spread is $10 wide ($60/$70) but the call spread is only $5 wide ($75/$80).

Taking this $60/$70/$75/$80 example further, if enough credit can be brought in to fully cover the narrower of the two vertical spreads (the $5 wide call spread), there would be no upside risk for the position.

To create a bullish bias in an iron condor, a wider put spread would be sold.

To create a bearish bias in an iron condor, a wider call spread would be sold.

Contract Size

Another way in which some traders will unbalance an iron condor is to begin with a standard or skewed iron condor but increase the number of contracts in one of the vertical spreads vs. the other.  To create a bullish bias in an iron condor, increase the number of contracts for the put spread.  To create a bearish bias in an iron condor, increase the number of contracts for the call spread.

For example, suppose a trader is entering a $55/$60/$70/$75 iron condor but wants to unbalance it through contract size in order to create a bit of a directional bias.

The trader could sell 1 of the $70/$75 call spreads but 2 of the $60/$55 put spreads to create a slightly bullish bias for the position.

Alternately, the trader could sell 2 of the $70/$75 call spreads but only 1 of the $60/$55 put spreads to create a slightly bearish bias for the position.

Iron condors allow great flexibility when it comes to constructing a position which will benefit from somewhat range-bound price action.

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Gamma is the rate of change in an option’s delta for a one-unit or point change in the underlying stock or index price.

One way to look at it is that the gamma is the amount of deltas which will be gained or lost with a one-point change in the underlying.  If the delta is the directional risk, the gamma shows how that directional risk will change as the market moves.  Therefore, delta would increase by the amount of the gamma with a 1-point increase in the price of the underlying, and delta would decrease by the amount of the gamma with a 1-point decrease in the price of the underlying.

The gamma will reflect how quickly an option changes its directional characteristics to behave more or less like the the underlying stock or index.  The higher the gamma, the greater the risk associated with the position.

Gamma will always be positive for long options and negative for short options.  It has the effect of creating deltas in the direction the underlying stock or index is moving.  The greater the gamma, the greater the effect on the position’s delta.  This results in getting longer (more positive deltas) as price increases, or shorter (more negative deltas) as price decreases.

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A collar is a hedging strategy whereby a position in the underlying stock is held along with two options which will cap gains and protect against losses. Both options are held in equal amounts and have the same expiration.

For a long stock position, the collar is constructed via a covered call (which caps upside gains) and a long put to protect the downside.

For a short stock position, the collar is constructed via a covered put (which caps gains on the downside) and a long call to protect the upside.

It’s common that both of the options are OTM, although not required.

Typically, this strategy is used by a trader who wants to hedge against any adverse move in the share price, while still allowing for a limited amount of additional gains in the position. It tends to be most effective when the trader feels the stock position has effectively run its course, but the trader is willing to allow for a bit more movement in either direction.

Some traders aim to establish collars with little to no cost, and at times for a small net credit. When a debit is paid to establish the collar, it tends to bring greater potential gain and reduced loss in the position. Collars which are done for credits tend to involve greater potential loss and reduced potential gain.

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