Philip M Halperin - Scribblings

 A Couple of Calculations Nobody Ever Makes  

  How do we close the Butterfly? Page 1
This part will be fairly trivial for anyone who has traded options or even learned about them academically, but please bear with me, because I am trying to build things up intuitively.    notes

Imagine for a moment a simple vertical ratio spread:

Long one 100 call,

Short two 110 calls

The profit/loss payoff of this position is well known. Ignoring premia at expiration, we have:

Fig 1_1 1x2 Vertical Call Spread

So the directional risk in this position begins at strike X and increases without bound with the underlying. So far, so trivial. Now, our geometric intuition tells us that X = 120. After this point the position begins to lose money. So the way to negate the unbounded nature of the risk is to buy one 120 Call:

Fig 1_2: 1x2 Call Spread + Closing Wing Call

Note that at 120, the long call profits negate the ratio spread position losses. The two positions sum to zero p/l above 120, leaving us with the well-known long call butterfly:

Long 1x 100 Call

Short 2x 110 Call

Long 1x 120 Call  

Long Symmetric Butterfly

  Here, again ignoring premia, we have a crack at making money anywhere between 100 and 120 and no losses that arise anywhere else. Period.  So, the vertical ratio spread can be closed in two ways (actually there are many other ways, but enumerating any of the others gets in the way of discussion at hand):

Buy back the spread itself

Buy the last wing of the butterfly.

So much for the introductory insight. We'll return to this point, but for the moment it is sufficient to note the following:

We can view a ratio spread as merely an incomplete butterfly.


next | top | Scribblings