Note 212The valuation seems not to take into account the expected rate of return of the underlying asset!This appears counterintuitive, but the probability of an up or down move is already incorporated in today‘s stock price.
It turns out, that the expected return needs not to be taken intoaccount elsewhere.The actual probabilities of up and down moves are irrelevant. What matters is the size of the two possible moves (the values u and d).I.e. the prices of derivative securities depend on the set of possible stock price paths but not on how probable these paths are.
Derivative securities: Options - Binomial asset pricing model