Re; - max-pain discussion, statistics - this gets deep!
To allow your range (in order to offset 'noise' effects?) is too grand. I think Ben's idea here is novel, but allowing +1/-1 of closest strikes doesn't pass the Z-test.
Umm. This bugged me for a week; I thought about it last weekend, and I think I know why.
Stock prices are a continuous spectrum ... or at least a close discrete approximation of continuity, given that the steps are small compared to the value. Therefore, statistical tools (such as a z-test) can give accurate predictions (correlation, standard deviation, etc.).
However, the steps in *option strikes* are at best 5% of the stock price, and at worst 10%. ($2.50 below $50, $5.00 above.) Worse, as the time value approaches zero, the distribution of each option price approaches its linear asymptotes, and is highly discontinuous (therefore non-integrable) at the "knuckle" exactly at the strike price.
So, using statistical tools designed for a continuous (therefore integrable) distribution on a discrete, discontinuous distribution may generate precision, but not necessarily accuracy. I don't think the data can generate a prediction more granular than what it is derived from (example - coin flips). So squeezing a prediction of a closing price to the closest nickel from data that is granular at 50 times that is futile.
However, when you look at the premise behind the max-pain procedure, I think you may have a point about how tight a predictor it is. Specifically, allowing the low range to go down to the next strike lower might be too generous; instead of a +1/-1 range, a +1/-0 or +0/-1 range may better reflect the spirit of the max-pain premise. I prefer, though, to use a looser range - because I am *more* confident that anything outside of it represents an opportunity. (The idea is analogous to the difference between a 95% confidence interval - 2 sigma - and a 99% confidence interval - 3 sigma.)
Thanks for the challenge to think through what had been more of a call on instinct than analysis ... I'm actually happier with my range choice than I was. (Assuming, of course, that someone doesn't shoot down my vaguely remembered statistical analysis ... <g>)
Comments and critique welcomed.
- Mitch |
