(a) Carefully define an arbitrage. (b) Suppose there are three complex securities i = 1, 2, 3 and two states k = 1, 2, where S; (k) denotes the time t payoff to asset i in state k : H 2 3 Si(1) 9 0 12 S1 (2) 8 6 So 5 4 5 Construct an arbitrage using the three assets above. (c) Given S, = 5 and So = 4, what is the arbitrage-free So in equilibrium? What are the AD prices? (d) What are the risk-free rate and the risk-neutral probabilities? Verify that the price of asset one is equal to the (risk-neutral) probability weighted expected return discounted by the risk-free rate