Question: Problem 3. Consider a binomial model with u = 1.2, d = 0.8 and periodic interest rate r = 0.1. Suppose that S = 10

Problem 3. Consider a binomial model with u = 1.2, d

Problem 3. Consider a binomial model with u = 1.2, d = 0.8 and periodic interest rate r = 0.1. Suppose that S = 10 at time t = 0. (a) (4 points) Find the possible values of the stock at time t = T. Is the model complete? (b) (6 points) Find the payoff at time t = T of a bull spread with exercise price K = 9 for the long call and exercise price K2 = 11 for short call. (c) (6 points) Find the replicating portfolio for the spread of question (b). (a) (8 points) Find the arbitrage-free price for the spread of question (b). Problem 3. Consider a binomial model with u = 1.2, d = 0.8 and periodic interest rate r = 0.1. Suppose that S = 10 at time t = 0. (a) (4 points) Find the possible values of the stock at time t = T. Is the model complete? (b) (6 points) Find the payoff at time t = T of a bull spread with exercise price K = 9 for the long call and exercise price K2 = 11 for short call. (c) (6 points) Find the replicating portfolio for the spread of question (b). (a) (8 points) Find the arbitrage-free price for the spread of question (b)

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