Serving the Quantitative Finance Community
Probability of being in the money
I recall reading that under Black-Scholes, N(d2) can be analogized as the probability the (call) option will be in the money at expiration. The actual language, however, left me thinking that it wasn't really the probability of being in the money, but more as a conceptual framework.So, is N(d2) truly the probability that the option, at maturity, would equal or exceed the strike price? If not, what is the formula (if any)?
Probability of being in the money
it's the probability in a risk-neutral world so you might want to do some more reading on martingales and change of measure
Probability of being in the money
it's easy to work out from scratch:price an option that pays 1 if the option expires in the money and 0 if it is out of the money.The value of that will be exp(-rt) * (probability in the money).If you have the BS formula, there are 2 terms: take the term that involves a factor of E (the exercise price or sometimes X) and divide it by E.That's the value of an the option I just mentioned