Hello,
I'm new to options (finance in general) and am trying to learn the theory.
I have read that the argument for why the underlying expected growth doesn't matter is that we're pricing the options relative to the underlying. That is, this information is already baked into the price of the underlying.
Fair enough, but then I started wondering why the same does not hold for volatility? E.g. in the binomial model, we have to explicitly input u and d.
Do stock prices not price in volatility (≈ risk)? From my understanding, by the CAPM (which I know is perhaps not always the most realistic, but in theory at least) only systematic risk should be rewarded. So if we then consider the theoretical value of the stock as some discounted value of future cash flows, where the discount rate is obtained via CAPM, volatility in the stock has SOME effect on the price? Is the explicit volatility parameter in the option pricing formula then accounting for the idiosynchratic risk NOT accounted for in the stock price? I don't believe this is correct, but I also can't help but feel like we then double count volatility, as it's both somewhat incorporated into the stock price, and then input again.
Thanks!