Some equations: ES1] ELS1] So = 1 + rrf + premium 1 + rcost of capital E.[S1] So = 1+ rrf = qubu + qaSa where qu(qa) is the risk-neutral probability of up (down) 1+ rrf call payoff = (ST - K) + A determined by making : (Call - A shares) = risk-free Problem 1 Suppose that the stock price follows the process: 130, actual probability = 70% So = 100 80, actual probability = 30% and the risk free rate is 5% over the period. Consider a call struck at K = 110. (a) (5 points) Find the payoffs at T = 1 in the up state (Cu) and down state (Ca) for the call struck at K = $110. Cu L ca(b) (25 points) Find the price of the call. You may use any method you like. Solution: Problem 2 (20 points, 5 points each) True or False. State whether the last sentence is true or false. No explanations are necessary; the grade will be based on the answer only. (a) Because we price calls with replication in the binomial pricing model, we do not need to know the expected payoff of the call in order to nd the price. Solution: (b) For the stock in Problem 1, the risk-neutral probability of up is 50%. Solution: (0) The A of the call in Problem 1 is 0.60. Solution: (d) In the binomial model, if the risk free rate is 0%, then it must be that the price of the digital up option and the digital down option add up to 1. Solution