There are stochastic discount factors, range of prices to be found.

Suppose there are three equally likely states of nature: expansion (E) normal (N) and recession (R). You have information about two assets (A and B) whose prices and payoffs as a function of the states of nature are given by the following table: State Asset Price Expansion Normal Recession (1/3) (1/3) (1/3) A 1 2 1 O B 1 0 1 2 (a) Find the set of stochastic discount factors (sdfs) for this economy. (10 marks) (b) Define when a payoff space and asset prices leave no arbitrage. Show that a positive sdf implies no arbitrage. (10 marks) (c) Find the subset of sdfs that imply no arbitrage. (10 marks) (d) Find the price of a bond that pays 1 in every state. (10 marks) (e) What is the range of prices for a European call option on asset A with strike price equal to 1 in the absence of arbitrage? (10 marks)