You are given: = 30, K = $31, r = 4%, T = 0.5, and = 2%. Let u = 1.2, d = 0.9, and n = 1.

(a) Using a binomial model find the price of a call option.

(b) Suppose that the European call sells for $2.50. Give a portfolio that can be used to take advantage of arbitrage and show that the portfolio you give is an arbitrage portfolio.

2. You are given: = 40, K = $39, r = 5%, T = 0.25, and = 2%. Let u = 1.3, d = 0.9, and n = 1.

(a) Using a binomial model find the price of a put option.

(b) Suppose that the European put sells for $1.5. Give a portfolio that can be used to take advantage of arbitrage and show that the portfolio you give is an arbitrage portfolio.

3. You are given: S = $60, K = $56, r = 5%, T = 2/3, = 3%, = 0.3, and n = 2.

(a) Find and and the risk neutral probability .

(b) Construct a binomial tree for the stock and find the price of an American call option.

4. You are given: = 25, = 1.2, = 0.9, = 6%, = 3%, = 1, = 2.

Using a binomial model, determine the premium for a 26-strike American put option.