Philip M Halperin - Scribblings
A Couple of Calculations Nobody Ever Makes
|How do we close the Butterfly? Notes|
In this and indeed most of my articles, I try to use the simplest examples I can construct. Partially, this is because I'm a pretty simple-minded guy. I tend to think from the inside-out, and I think it's easier to read stuff that is presented in that manner as well, inferentially. I believe in Okham's Razor --- do not multiply entities beyond necessity. And multiplying examples beyond necessity can only get in the way of inferential logic.
So, the term "butterfly" will refer here to the simplest form to understand - a long call butterfly, where we are long one strike, short in the middle, and long at the end. Again, for simplicity, I strike the first long call at 100 and the first short call at 110.
Yes, we all know that a put butterfly with the same strikes and weights will have the same characteristics (if European), and yes, we are aware that in some markets (such as OTC FX options) "butterfly" refers to a Call-Call-Put-Put combination, sometimes called and "iron butterfly" or "criss-cross" elsewhere.
But what we are trying to get at here is the calculation of the generalised butterfly and a ratio spread trading strategy that follows therefrom, so we will use the long call fly as a point of departure, and call it the butterfly. For the short butterfly, rotate these graphs about the horizontal line. For the put fly, work from right to left in building it up. You get the idea. back
|I might develop this topic later on, but I would like to make a crack or two about visualising geometry. One of the side-effects of the ubiquity of digital calculators and now computers is that the folks who have grown up with them have never really developed the "feel" for numbers in the same way that previous generations of punters have. I claim that an option is a functional response surface in hyperspace with too many dimensions to be able to summarise any other way than geometrically. Yes, the greeks give us point estimators, and yes, these can be shot out of a computer with incredible velocity. But a trader who relies purely on the computer output and proceeds to dynamically hedge mechanistically is at a tremendous loss when compared to a trader with the geometric intution of how the real response of his position behaves. With the geometric vision of the response, he (or she --- and I do think that women are naturally better at this) can see what is happening to the positions, and, better still, what might happen, and therefore has a much greater range of possible responses and correct reactions to whatever might befall the position, than he (or she) would if armed only with the ceteris parebus set of partials and cross-partials that come for a penny a pound today.
For options are a geometric phenomenon, and when you get beyond simple puts and calls, the geometry can get quite complex indeed. Any price-taker who has control of the geometry of the position should be able to use that geometry to advantage.
Looking at it another way --- could you drive your car if you had to rely purely on the speedometer, a compass, and other instruments? Or do you prefer to get a feeling of how things are going by taking a visual look out the windscreen? Do they even certify pilots who cannot make visual landings, and would you knowingly choose to fly with one, no matter how good the in-flight cinema? QED. back
|With the black humour characteristic of futures options traders, this construction somehow was named the "Butafuoco" in the Chicago pits of the early 90's.
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