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Optionetics Commentary

TRADING FLOOR SECRETS: Butterfly Mechanics and Pricing


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Scott Kramer, Optionetics.com
February 19, 2006


I have been bombarded with emails about butterfly spreads, and most usually politely asked to write something about them. There was also mention of butterfly spreads done for a credit or free.

Firstly, a butterfly spread can be defined as the purchase of a call/put vertical spread and the sale of a call/put vertical spread sharing a common center strike. The center strike that is shared is known as the body and the other strikes are referred to as the wings.  As their use arrived before that of stealth bombers they were referred to as butterflies, but had they originated during the present they would likely be termed stealth bombers as their profit and loss graphs look much like the F-117 as the insert below shows.


How this ominous profit graph comes about is by the arrangement of the strike prices. You will always be buying the vertical spread that is closer to ATM (at-the-money) or deeper ITM (in-the-money) and sell a vertical that is further OTM (out-of-the-money). Using the graph above shows that it is a purchase of the 35-40 call spread (buying the 35 call and selling the 40 call), then selling the 40-45 call spread (selling the 40 call and buying the 45 call). Believe it or not, the graph illustrates the same thing using put options. This could just as well be the purchase of the 45-40 put spread buying the 45 put and selling the 40 put) and the sale of the 40-35 put spread (selling the 40 put and buying the 35 put).

Buying the 35-40-45 call butterfly for $0.20 will result in the same profit as buying the 45-40-35 put butterfly for $0.20 regardless of where the stock closes on expiration. Some reading this will not believe the last statement, but if you do the math you will find it to be absolutely true. Then why do one over the other, that is, call vs. put spread?

Most butterfly spreads are done when the stock is just entering one of the strikes. Using the same example, if a stock was at $36 and you were slightly bullish you would most likely do the call butterfly. If the stock were at $44 (for example) and you were bearish, the put spread would be favorable if for no other reason than most want to avoid the early exercise risk of having deep ITM options placed to open a trade; other than that, though, neither if favorable over the other.

So how does this look on expiration? The table below illustrates the value (not the profit and loss) of a butterfly on expiration at varying stock prices. 

Stock price

$0.00

$32.00

$35.00

$36.00

$37.00

$38.00

$39.00

 

 

 

 

 

 

 

 

Butterfly pieces

Long 35 call
1 contract

$0.00

$0.00

$0.00

$1.00

$2.00

$3.00

$4.00

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Short 40 calls 
2 contracts

$0.00

$0.00

$0.00

$0.00

$0.00

$0.00

$0.00

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Long 45 call 
1 contract

$0.00

$0.00

$0.00

$0.00

$0.00

$0.00

$0.00

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Net butterfly

$0.00

$0.00

$0.00

$1.00

$2.00

$3.00

$4.00




Stock price

$40.00

$41.00

$42.00

$43.00

$44.00

$45.00

$50.00

 

 

 

 

 

 

 

 

Butterfly pieces

Long 35 call
1 contract

$5.00

$6.00

$7.00

$8.00

$9.00

$10.00

$15.00

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Short 40 calls
2 contracts

$0.00

-$2.00

-$4.00

-$6.00

-$8.00

-$10.00

-$10.00

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Long 45 call
1 contract

$0.00

$0.00

$0.00

$0.00

$0.00

$0.00

$5.00

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Net butterfly

$5.00

$4.00

$3.00

$2.00

$1.00

$0.00

$0.00

There use to be a time in the 1970s and ‘80s when you could do butterfly spreads fairly easily for a credit, as no one really understood what they were. The markets have grown up. You can thank Bill Gates and Steve Jobs for this. Technology has made the markets more efficient than ever. It is difficult to buy butterfly spreads for free any longer (let alone a credit), but occasionally they can be done if you take a momentary leg correctly.

For this legging into butterfly spreads for close to free you have to do the trade in an very volatile stock or in an index. It is almost impossible to do a butterfly for close to free in a typical equity. The reason for this is primarily the distance between the strike prices as a percentage of the underlying. Index options will often have strikes less than 1 or 2% apart, while the typical stock may be 10% apart. The example above with $5 strike prices on a $40 stock represents a distance 12 ˝% distance between strikes.

Since then some of the more sophisticated traders have devised ingenious ways of bending butterfly positions by playing with the strikes and quantities to essentially do the same thing; that is, get essentially butterfly spreads on for free, though your broker will argue that they are not the same.

Due to the likelihood of a stock moving away from the center strike, the area of greatest profitability, butterfly spreads will not trade near their maximum value (even if the stock is hovering in the middle strike area) until a couple of days before expiration. Think about it. Why would you pay close to $5 for a $5 butterfly when that is the maximum that could be made but several days remain where the stock could move enough to have the spread expire worthless?

The question I am getting is, “how much do you pay for a butterfly?” There are too many variables to address in an article this size which dictate what a fair value for a butterfly is, especially when it comes to equities. This could obviously be an entire course by itself.  Indexes are a little easier to address. I am hearing of some scary instances where people are paying $0.15-$0.20 for a $1 butterfly in an index such as the DJX with a month remaining until expiration. I recommend that you do not do this unless either:

  1. You need a tax write off. 
  2. You have a crystal ball and know where the index will close on expiration 
  3. Or you have a really good reason, like someone recommended you do it.

I am obviously being facetious with at least one of the above reasons (hint: number 3). The easiest way to learn what is a fair price to pay is not by going off the bid/ask spread. Butterfly spreads can be bought as a package for considerably cheaper than the “natural” of giving up the bid/ask price. Typically, if the option prices are fairly priced, the spread will be trading for roughly the middle of the bid/ask spread. The easiest way is to get the theoretical value of the individual options and use that to determine what the spread is worth. If you don't have access to decent theoretical and want to trade butterfly spreads, I would recommend getting some as the price of the software will possibility be made up on not overpaying on your first butterfly alone.

Time to fly,


Scott Kramer
Staff Writer and Trading Strategist
Optionetics.com ~ Your Options Education Site
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