OK, I admit that this is a frequently asked question. But I couldn't find a satisfying answer after I read the explanations of books, went through the derivations of B-S formula, and searched answers online. My question is that, I can understand the derivation of the B-S formula, but what is the intuition that the expected return rate of a stock has nothing to do with its option price?
Suppose I have two stocks A and B, the price is the same today, both worth 20 dollars. Stock A has a expected return of 0.5 dollars/week, a volatility of 50%; stock B has a expected return of 10 dollars/week, a volatility of 1%. For call options with strike price 40 dollars expiring in 1 month(4 weeks), how can the option price for stock A is greater than that for B, since stock A is expected to worth only 22 dollars while B is worth 60 dollars? Any intuitive explanations?
I can also make examples where stock A has vanishingly expected return and B has infinitely large expected return.