Suppose there are three equally likely states of nature s {1, 2, 3} that might...

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Suppose there are three equally likely states of nature s € {1, 2, 3} that might occur at date t + 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 t + 1, are given by the following table: Asset Bond Stock State Price 1 2 3 1.00 1.00 1.00 1.00 1.00 1.50 1.00 0.50 (a) 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 t + 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 t for a European call option on the stock with strike price equal to 1 that matures at t + 1. (10 marks) Suppose there are three equally likely states of nature s € {1, 2, 3} that might occur at date t + 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 t + 1, are given by the following table: Asset Bond Stock State Price 1 2 3 1.00 1.00 1.00 1.00 1.00 1.50 1.00 0.50 (a) 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 t + 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 t for a European call option on the stock with strike price equal to 1 that matures at t + 1. (10 marks)

Answer rating: 100% (QA)

a To find the set of stochastic discount factors SDFs for this economy we can use the basic pricing equation for the bond payoff and the stock excess ... View the full answer