(8) Options. We come up with the following model for the stock of Shake Shack (SHAK). The stock price is 67$ today (t = 0). An analyst predicts that in a year from now (t = 1) the outcomes are S(1) = 100$ with probability P 258 with probability 1-p The annual interest rate is 2%. (a) Calculate the forward price F of the stock. (b) Calculate the price C(0) of a call option on SHAK with delivery date t = 1 with a strike price 50$. (c) Calculate the price P(0) of a put option on SHAK with delivery date t = 1 with a strike price 50$. (d) Calculate the return of the above call option. If p= 1/2, what are the expected return and the standard deviation of the return