• Long one put.
• Short two puts further out-of-the-money (at a lower strike and lower delta).
• Long one put very deep out-of-the-money.

<BWB risk graph retrieved from OptionStrat>

A trader would want to use a broken-wing butterfly if expecting the price to expire very near where the two short puts are (but with a directional bias leaning to one side). 

Intermediate: Practical Application

As a general caution with this strategy, do not be fooled by the intrinsic value on the risk graphs because you must cut it very close with time in order to go anywhere near max profit. There are not many good risk cases for continuing to play chicken with time after already winning price-wise with a pin.

As an example of a pinning strategy in application, opening a broken-wing butterfly on top of a Call Wall could be a logical approach if placing a wingtip above the wall. The idea of doing this is based on how Call Walls tend to be breached mildly before the price drops back down. 

Another use case would be to pin the short options pair on top of Absolute Gamma, but then to set up the longer wing on the side where one has a slight directional bias of which way the price might be more likely to drift away from the pin.

Advanced: Customizing the Wings

A broken-wing butterfly is a deviation from a normal butterfly in that it is tweaked in a way customized for a specific trade thesis by moving one of the wings further away. As pictured above, with two short options at the center, one of the long wingtips can be moved further out. 

This reduces the max loss and overall cost of the trade. But if one wing is stretched too much then it can present a dangerous risk because this could substantially increase max loss for only a minor cost reduction. In this scenario, the long put of the lower strike is further out-of-the-money and therefore unable to protect the position as well if the underlying security drops sharply.

Expert: Variations and Synthetics

As a general synthetic principle, calls can be swapped out for puts here, and vice versa, if long is swapped for long and short is swapped for short on the same strikes.

In contrast to a long BWB, which would want to land in one of two directional regions (but not right on a specific pinpoint range of the price), a short butterfly does not dilute the potential reward benefits across two separate regions. Instead, the short BWB concentrates that potential benefit in one place.  

What makes one wing “broken” is that the butterfly spread is asymmetrical and the center of it is closer to one side than the other. In other words, one wing is shorter, as if it were broken.

An alternative way to break a wing on a butterfly is to remove one wingtip entirely, but this would open up a case for undefined risk (unlimited loss). At this point, it would become a frontspread (more short contracts than long). Therefore, a BWB is like a frontspread but one that uses a wingtip to keep its risk defined.

Absolute Gamma: Absolute Gamma is the strike with the largest total gamma. It can be treated as a strong support/resistance level and a magnet. It is also normal for this level to be near an inflection point like Zero Gamma rather than near the far edges of the trading range. 

butterfly spread: A butterfly is a type of option strategy with a limited max loss that is either betting for or against a stock or future to have little to no price movement (often called a “pin”). If betting for a pin, then it is counting on a trade to end up in a specific narrow range. If betting against a pin, then the strategy gets paid if it ends up anywhere except for where the pin is. Another characteristic of butterflies is that they tend to have a very low max profit until the moment of expiration, which makes them difficult to hedge. 

Call Wall: The Call Wall is the strike with the largest net call gamma. This shows us what the top of the probable trading range is (the upper bound).

defined risk: In an option strategy, if risk is defined then it is structured so that it has a max loss (capped total loss on a trade) rather than potentially unlimited loss.

frontspread: A frontspread is a type of ratio spread (uneven amount of long and short contracts) where more options are sold than bought. A call frontspread sells more calls than it buys. Likewise, a put frontspread sells more puts than it buys.

long call: To be long (buy and hold) an option contract which has limited risk and unlimited potential gains from moves up in the underlying price. The max loss is the cost of the call. Going long on a call is a simple way to gain upside exposure to movement in an underlying security, however the underlying security (such as a stock) must outperform the premium placed on that call by the options market. In other words, a long call must beat the options market in order to profit. If closed early (well before expiration) then a long call must outpace the expected move (priced in by the options market) for a specific period of time. All long calls have long gamma and long vega but short theta. It is uncommon to exercise calls rather than simply close them for a profit, however a long call is frequently understood as a right to exercise (trade in the long call to be long 100 shares) if above the specified strike price. Synthetically, a long call becomes logically equivalent to a long put if also short 100 shares.

long put: To be long (buy and hold) an option contract which has limited risk and amplified potential gains from moves down in the underlying price. The max loss is the cost of the put. Going long on a put is a simple way to profit from  downside exposure to movement in an underlying security, however the underlying security (such as a stock) must outperform the premium placed on that put by the options market. In other words, a long put must beat the options market in order to profit. If closed early (well before expiration) then a long put must outpace the expected move (priced in by the options market) for a specific period of time. All long puts have long gamma and long vega but short theta. It is uncommon to exercise puts rather than simply close them for a profit, however a long put is frequently understood as a right to exercise (trade in the long put to become short 100 shares) if below the specified strike price. Synthetically, a long put becomes logically equivalent to a long call if also long 100 shares.

OTM: An option is out-of-the-money if it would have zero value expiring with the underlying at its current price. When an option is out-of-the-money, its entire price is made of extrinsic value, which is a premium that option buyers are willing to pay for an opportunity to make a profit.

pin: A pin is a thesis or a condition where prices tend to stick in a narrow range. A pinning condition is usually linked to high gamma levels in the market. The Absolute Gamma strike is a normal place for a pin to occur. The phenomenon of a pin is how a security is drawn to a specific price as it nears expiration. Technically, when approaching an expiry and when close to an option’s strike, the increase in market gamma creates dealer hedging activity which causes the stock to gravitate back to the pinned strike; dealer hedging is the rebalancing of market maker books to neutralize their risk.

short call: To be short (sell to open and hold) a call. Unless otherwise hedged, the owner of the short call has unlimited risk and only limited potential gains, which makes this an extremely dangerous strategy in isolation. If left to expire, a short call will achieve max profit if the price ends up underneath the strike price. Shorting a call is a way to express a thesis that one is “not bullish” such as what might be justifiably the case if testing a Call Wall from underneath; being “not bullish” is different than being bearish. For a short call to be profitable, the underlying security must underperform the premium placed on that call by the options market. In other words, a short call profits when the underlying security fails to beat the options market. To be closed early for a profit, there needs to be a decrease in implied volatility or the underlying must have increased less than the options market has priced in for that specific period of time. All short calls have short gamma and short vega but long theta. Short options also come with obligations instead of rights, which means that, at any time, shares can be assigned (100 short shares for each contract); assignment usually only happens when in-the-money and near expiration). Synthetically, a short call becomes logically equivalent to a short put if the trader is also long 100 shares.

short put: To be short (sell to open and hold) a put. Unless otherwise hedged, the owner of the short put has severe risk and only limited potential gains, which makes this an extremely dangerous strategy in isolation. If left to expire, a short put will achieve max profit if the price ends up above the strike price. Shorting a put is a way to express a thesis that one is “not bearish” such as what might be justifiably the case if testing a Put Wall from above; being “not bearish” is different than being bullish. For a short put to be profitable, the underlying security must underperform the premium placed on that put by the options market. In other words, a short put profits when the underlying security fails to beat the options market. To be closed early for a profit, there needs to be a decrease in implied volatility or the underlying must have fallen less than the options market has priced in for that specific period of time. All short puts have short gamma and short vega but long theta. Short options also come with obligations instead of rights, which means that, at any time, shares can be assigned (100 short shares for each contract); assignment usually only happens when in-the-money and near expiration). Synthetically, a short put becomes logically equivalent to a short call if the trader is also short 100 shares.

strike: The price that an option is based on. A long call will expire worthless if the price of the underlying security finishes underneath the strike price, and a long put will expire worthless if the underlying finishes above the strike price.

synthetics: In options, synthetics are different structures that have the same logical dynamics, including the same max loss, max profit, chance of winning, and option Greeks. Synthetics are possible because options have the property of put-call parity. For spreads, long puts can be swapped for long calls and short puts can be swapped for short calls (and vice versa) in a way that creates synthetic matches without the need of adjusting deltas with shares. On single-leg options, however, puts and calls can be swapped in the same way, but require directionally-offsetting positions in the underlying security (such as a certain amount of shares).

wingtip: A wingtip is what we call the endpoint of an options strategy where it is furthest out of the money (OTM). A reference to a wingtip is always to the furthest-OTM strike in a strategy. If the main leg on a vertical strategy (both options on the same date) is a credit (a premium is received for taking on some risks and potential obligations), then a long-option wingtip protects against some short gamma risk (directional risk that can increase and accelerate). The cost of defining the risk is giving up some of the premium collected. In order for risk to become defined with main credit legs, then at least as many further-OTM long contracts would need to be written.