Hello, Suppose you see options on five different stocks, each with a probability in the money of 10%. Can you actually use classical binomial distributions with this information? If so, then the probability that exactly two of them will land in the money would be: (5C2)(.1^2)(.9^3) = 7% Can we really do reasoning like that?
I don't think you would want to use a binomial distribution to model probability that more than one stock will be ITM but I could be wrong. I think the other issue is that you're assuming the stocks returns aren't correlated but they probably are.
Q: how much can you rely on "probability in the money" calculations? A: Zero. For the obvious reason that if you could rely on "probability in the money" calculations you would become a millionaire very quickly. Options 101 - There is no free lunch.
Probability of the calculation will derive from the implied volatility - usually ATM, but the really good tools do it from multiple implieds. Is it good? Sure it's OK and as good as of an estimate as exists under current pricing theory. Fundamentally it's the same expectation as was used to create a theoretical value for the option. So if I buy an ATM it has about a 50% probability of finishing ITM and about a 50% of not. Take all those probabilities and you get a price for the option. Will it help you make money ? The reason you buy an option is because you have some expectation about price. In a two dimensional world - a simple view - buys are hoping actual volatility exceeds implied. So the realized moved is larger than the expected move. Does that make the probability calculation valueless - NO. Volatility can change over the life of your holding, but every option trade is about a volatility assumption - the marketplace thinks the most common event defines some expected range. If you disagree you might choose to buy options. If you agree or believe it is too large you might sell options. Again that's overly simplistic, but I can use the volatility to create an expected value for every possible price of the underlying. In fact that is what the binomial pricing tool do. Again overly simplistic, but it ain't the worst estimate. Also their is actual friction in the trade so you don't trade at actual theoretical. A lot of noise goes into the pricing assumption when carry gets big and for longer dated options.
I don't think OP has said anything about there being a free lunch... I'm sure he realizes that you pay premium for the probability... Actually... If I would take your statement regarding reliability of probabilities being zero,... that would mean that the implied vols also have zero reliability, are therefore completely inaccurate and shouldn't be used to compute options pricing... something I have to strongly disagree with. But I guess that's beyond your Options 101 course....
I have seen them on IB and TOS. I find they are only reliable until they are not. I've seen Options with 100% probabilities of OTM to be ITM in the face of extremely sudden events. I think these probabilities are calculated assuming the same Implied volatility carried into the future. I stand to be corrected.
Obviously that's more or less correct. Look, there's never really a 100% chance... there's always a 0.1% or lower chance that a stock goes -50% or more... even if IV is relatively low. That's the tail risk bit... the probability is there but so low, that it seems zero. That there should be reason to not sell options at 1 cent en masse... it will backfire at one point in time and the proceeds will likely not cover the losses. Does that mean you should buy all those options? No... I don't think so either... since you don't really know when that event will happen, and in the mean time you're pissing away cents. It's like a fringe thing.... yes/no/meh... Also, I think the further OTM you get... the less those probability of ITM means anything. Vols mean less the further out you go... but there's still some logic to it.
I mainly use those probabilities when I write options. If you buy options, in IB, it will actually show you new probabilities when you click on "Performance Profile" and it's totally different from the probabilities shown when writing options.