3. (17%) The current stock price of FB is $29. Alex expects that in one year the stock price of FB will be either $40 (up move) or $20 (down move). The exercise price of one-year European put option of FB=$30 and the one-period risk-free rate rf = 2% per annum (NOT rc). Also, investors can freely trade (either buy or short sell) the GS fund, {200 units of FB European put option + 200 shares of FB stock}, and the MS fund, {N shares of FB stock + risk-free one-year CD with original investment $B} in the market. That is, no arbitrage opportunity exists. (a) (3%; 3%) Find the gross payoffs ($) of the GS fund in the up and down move, respectively. (b) (3%; 3%) The GS fund and MS fund have the same future payoffs in one year. Find the values of N and B. (c) (3%) Calculate the current price ($) of European put option of FB (per unit). (d) (2%) If the GS fund is perfectly equivalent to the MS fund, then we can see {200 units of FB European put option}={short sell Y shares of FB stocks + cash $C}. Use this idea to calculate the equivalent percentage margin (%) for 200 units of FB European put option. (Note: Percentage margin=(equity)/(short position)).