The BlackScholes formula for option prices uses the risk neutral probability, which uses the riskfree rate. The same is with binomial trees for pricing option, you use the riskfree rate to derive the risk neutral probability. But this is all when pricing options.
If you want to know the expected payoff of the option at the end, or the probability of the option paying off, or the probability of a stock being above or below a certain price, you use the expected rate of return, either in the lognormal formula (which will then be just like the BlackScholes formula for d1 and d2, just with expected rate of return replacing the riskfree rate), or in the binomial probability formula for binomial trees (but keep in mind for calculating u and d in the binomial trees, you still use the risk free rate).
Last edited by disluckyperson; Today at 03:00 PM..
