Pretty much every article I read on options and option pricing, they lead you to believe that the option price is based on the current spot price. For example, option prices are based off what Apple is trading right now. Is this true?
My understanding is that the option price is actually based on the forward price of Apple with the same expiration as the option itself. So an option is actually priced off the current apple stock price adjusted by e^(rt). Same with options on futures. The option on a future is based on the forward price of that future, not the future itself. Now, the forward price of a future tends to be similar if not the same as the future as carry costs for a future are minimal so r is close to 0.
Is my understanding correct? If that's true, doesn't that mean that every option expiration is based on distinct underlyings (respective forward prices), not just one underlying (whatever the prevalent spot price is).