I have S(T) = 500 if stock up and 350 if stock goes down . If K =400, then the payoff C(T) of call option is $100 if the stock goes up and 0 otherwise ( when not exercising the option ). And suppose the premium C(0) is let's say $51. What is the expected return of the call option E(Rc)and std deviation of the return if p and q (1-p) are 0.5 each .
Should I say that Rc (return of call option) = 100 - 51 / 51 = .96 if stock goes up and 0 - 51/51 = -1 if stock goes down which lead to E(Rc) = 0.96 * 0.5 + (-1) *0.5 = -.02
Or simply Rc = 100 if stock goes up and 0 if stock goes down which lead to E(Rc) = 0.5 * 100 + 0.5 * 0 = 50
Please help
