A question about European call option, stochastic discount factors, the basic

pricing equation for the bond payoff

Suppose there are three equally likely states of nature 3 E {1, 2, 3} that might occur at date 15+ 1, the assumptions of free portfolio formation and the Law of One Price hold. There are two assets whose prices at date t and payoffs, as a function of the states of nature at date 15+ 1, are given by the following table: State Asset Price 1 2 3 Bond 1.00 1.00 1.00 1.00 Stock 1.00 1.50 1.00 0.50 (3) Find the set of stochastic discount factors for this economy. (Hint: write the basic pricing equation for the bond payoff and for the stock excess return.) (10 marks) (b) Explain when a payoff space and asset prices leave no arbitrage and find the subset of stochastic discount factors that imply no arbitrage. (10 marks) (c) A European call option on the stock that matures at 13+ 1 gives the right to buy the stock at date t + 1 at the strike price. Obtain the set of no arbitrage prices at date If for a European call option on the stock with strike price equal to 1 that matures at t + 1. (10 marks) (d) Find the stochastic discount factor with minimum variance. (10 marks) (e) Use the stochastic discount factor you found in (d) to value two projects with payoffs 11:1 : (150,025,150) and .1132 : (125,1,1). Does the value of these projects reflect compensation for risk? Explain. (10 marks)