Quote from scienter:
Is their a common model at OX or available on the web that is used that you are aware of?
Well, the normal models apply e.g. Black Scholes, Cox Ross Rubinstein etc.
However, most places, like OX won't output the probability value from these models. To be honest, the difference between calculated delta and probability is entirely dwarfed by the flaws and assumptions in said models as well as the garbage in, garbage out factors, so I wouldn't worry about it too much - it's more a piece of academic useless information.
If you have access to the ToS platform, you can compare delta alongside probability to see the differences.
I guess that what I was referring to originally when I asked about a "point of reference" from which sigma would be calcualted from. So, using todays closing level of approx. 1280, if I wanted to wait for a 1 sigma move b/f placing my spread, how would I calculate it, esp. if I want to use IV to calcualte it instead of statistical/historical volatility?
If not already done so, I would recommend reading Natenburg's Option Volatility and Pricing. If anything, just reading chapter 3 and 4 in a book shop or library would be beneficial.
To answer your question 1 sigma = 1 standard deviation = volatility (annualized). They are virtually interchangeable.
e.g. if ATM IV is 10% that is telling you that 1 sigma/standard deviation is 10% and the market thinks (implied) that a year from now we will be trading at 1280 +/- 128 points 68%ish of the time (close to close). Ignoring interest rates/dividends etc.
A one sigma move in this context is therefore 128 points.
Knowing that standard deviation is proportional to the square root of time allows you to approximate volatility (standard deviation) values for different time periods.
Back of envelope calculations:
Daily volatility can be approximated by annualized volatility/16
Weekly volatility can be approximated by annualized volatility/7.2
Monthly volatility can be approximated by annualized volatility/3.5
(Implied) Volatility for just the period leading up to expiration can be approximated by pricing an ATM straddle. This will give you a $ amount rather than a % obviously.
For all of the above, they are saying: during X time period, the underlying will trade +/- volatility value 68% of the time. OR for about 2 out of every 3 of X time periods the underlying will move by +/- volatility (close to close).
Thus, you can think of implied volatility as implied sigma or implied standard deviation.
I would recommend not entirely dismissing historical volatility as a tool to balance what you read from IV.
Would it be horribly wrong if I were to look at the delta's for underlying calls and puts tonight and identify those strikes at .32 and say..ah hah.. . you little bastards, if on Tues the market were to move to your stike levels, we have experienced a 1 sigma move?
Using the information I outlined above, you can decide whether this is reasonable or not!

Good luck!
MoMoney.

