I recently met an options trader that said to me that the price of an option is the expected present value of the payoffs of an option (present value as in discount by the risk free rate and expected value as in real world not risk neutral probabilities).
Anyway I tried to demonstrate to him why this approach is flawed. So typically most books eg Mark Joshi's Concepts and Practice of Mathematical Finance (which is a fantastic book in my opinion) demonstrate why this is wrong by constructing an arbitrage opportunity.
Unfortunately the options trader just dismissed it and started telling me about what Black, Scholes and Merton did...
So my question is there a reference where Black, Scholes or Merton actually say that this is not true in their original framework?
EDIT A more recent survey paper written by them or something along those lines would also be extremely helpful.