Suppose you consider a call on a stock with strike K and time to expiration T. We consider the stock price at time T as a random variable ST. What is the fair value c of the call in terms of an expectation of a suitable random variable if we use the approach in (a) (and ignore interest rates and discounting)?
Note: This Method in (a) was "You play a game where you have to pay an upfront cost C to enter the game. You cannot lose any more money and your gain depends on the value of a real-valued random variable Y. Namely, if Y is negative, then you do not gain anything. If Y is positive, then you gain the amount Y. What is the fair value of C, i.e., the value C where on average (when you play the game repeatedly, one game does not influence the following games, and you do not care about the risk involved) you neither gain nor lose money in the long run?"