Sorry, looking at that slide rule brought back a flood of boring memories and I fell asleep! But seriously, if you have the patience to explain these formulas to me I'd be grateful. What I think I know is: Delta = the amount the option moves for every $1 movement in the underlying. So I guess if the Delta is .25 there's a 25% chance of the option price making the Strike price, because the option moves 4 times slower than the underlying trying to get there. Prob. ITM = Mostly Historical Volatility/Standard Deviations (like you originally said), or else they wouldn't have a separate % number for Implied Volatility. So here they are indeed trying to predict future movements based on an average of past movements. Impl Vol: What traders have voted on (via their Ordering, Buying and Selling of the Option in question) as to how they think the Option will move in the future. It has something to do with "68% of the time" as well, but doesn't allow for the other 16% + 16% before and after the middle of the curve, etc. So to answer your question, No, I don't see how IV changes everything else, because I thought all 3 things were separate from each other! Please explain further... Thanks.
Delta is affected by IV because, if IV goes up, traders feel the market will be more volatile. A more volatile market means a higher probability of your strike being touched, thus delta of it goes up. This is all in the Black-scholes formula. Delta and all the other greeks are dependand on the IV input. BS also assumes normal distribution when calculating deltas, although some of the fat-tail risks are ocmpensated for via higher IVs below the current mkt. All in all, I wouldn't use delta or any mathematical formula for probability calculation like this, I actually backtested selling 5 delta strikes throughout 2011, statistically they should've been hit only 5/100 = 5% of the time, but they got hit much more often than that. As someone else said, you're better of looking at macroeconomic figures, and clear support/resistance/trend levels.
And Implied Volatility is the same as the $VIX, which is a computation based on the sale of Puts? The "Fear Guage"? If so, what about the sale of Calls? They must count too for the Delta to go up when traders are optimistic.
Impled Volatility is not the same as the VIX. Implied Volatility is unique for each and every option in the market depending on its underlying supply/demand. The VIX on the other hand, is a general measure of volatility accross the board.
Delta is N(d1). The risk-neutral probability of expiring ITM is approximately N(d2). Since d2 is strictly less than d1 (by sigma*sqrt(T-t)), delta will always overstate the true risk-neutral probability.
Well duh! What's the point in stating the obvious? Talk about risk-neutral probabilities,... the end result of which, will be the obliteration of one's portfolio, mass hysteria, world wide flooding, and the end of civilization! http://www.flixxy.com/trumpet-solo-melissa-venema.htm
If you use an Option Model to calculate Probabilities, then it will suffer from the same limitations and caveats that ALL Option Models do ... but at least it will be consistent with all the other Greeks that the Option Model generates ... Espen Haug covers PROBABILITY GREEKS in his book 'Option Pricing Formulas' and suggests that the Greek he calls STRIKE DELTA can be interpreted as the discounted risk-neutral probability of the Strike ending up In the Money ... similar to the Delta Adjustment that Kevin mentioned above .... Back to the real world .... in practice, I use one of three methods as rough and ready approximations .... 1. The absolute value of Delta approximates to the Strike finishing ITM ... the shorter the time frame / the lower the Vol / the more accurate the approximation. 2. ATM Straddle Price x 1.25 approximates to 1 Standard Deviation Move 3. Max Loss / Strike Width % for a Vertical Spread approximates to the Strike finishing ITM Whereas 1. uses an Option Model ... 2. and 3. have the advantage of using Liquid Market Prices ... Hope that helps Cheers James