Donnap's example was a 3 years call vol=5% in a BSM world 
delta depreciation
- Thread starter saminny
- Start date
Theoretically, it is the probability of the option expiring in the money however it does not consider any market risk. Here is BSM interpretation I found:
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N(d1) and N(d2) are the probabilities of the option expiring in-the-money under the equivalent exponential martingale probability measure (num�raire = stock) and the equivalent martingale probability measure (num�raire = risk free asset), respectively. The equivalent martingale probability measure is also called the risk-neutral probability measure. Note that both of these are probabilities in a measure theoretic sense, and neither of these is the true probability of expiring in-the-money under the real probability measure. In order to calculate the probability under the real ("physical") probability measure, additional information is required�the drift term in the physical measure, or equivalently, the market price of risk.
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What is the probability that a call ends in the money? Is it 0.5?
Sometime.
Did you have the idea to think about the question in the first place? How sure are you that your set of the "unknowns unknowns" is not empty? What if your set of "unknowns unknowns" is a subset of "knowns knowns" in the hand of your opposition in the option's market?
My set of "unknowns unknowns" is definitely not empty, and even if it were empty, I would be stupid to assume it is empty unless I can prove otherwise---which I find is an impossible task.
I find it more difficult to pose an unknown question than to answer a known question. For me, posing a question is 99% (or a large number) of the answer.