Exercise 1. [2|] points}{No picking numbers} lClonsider a stock that pays no dividends on which a futures contract, a caJl option, and a put option trade. The maturity date for all three contracts is T, the strike price of both the put and the caJl is K... and the futures price is F. Prove that if K = F... then the price of the call option equals the price of the put option. Solve for both short and long future. Exercise 2. [1|] points}3uppose a stock pays a dividend yield of 1% annually. [ts current value is 32%|). The Thill rate is 4%. Suppose the future price for delivery in 1 year is $2050. lfi-onstruct an arbitrage strategy to exploit the mispricing and show that your prots 1 year hence will be equal to the mispricing in the futures market. Exercise 3. {21] points) The Ail-11's Paradox. Consider three alternatives c1 = 5mg = l,n3 = fl. Lottery L1 E [I]? Lil} implies probability of getting .11 is U, probability of getting .12 is l, and probability of getting .13 is I]. Let L'l E {.l,.89..l}? L2 E (D, 0.113.391}, L; E [n.1, n, [1.9). Suppose and expected utility maximizer prefers L1 over Li, then what should be his preference over L2 and LE. Read about Allais paradox and expected utility. Provide explanation for your