3.[8 points] Consider a 2-period CRR model with d= 0.9, r = 5%, u = 1.4 and S(0) = $100. The stock pays a $23 dividend at time 2. Consider the American call option with strike $100. (a) (4pts) Draw the payoff tree and calculate the pricing tree. At what node is the call executed before maturity? (b) (2pts) At the node from a), the option holder wants to wait and ask to change the American call into a European call with the same strike price. Using B(0) = $60, what would be the replicating strategy (80, 81) for the European call? (c) (2pts) How much refund would the owner get from changing the American call into a Euro- pean call? Check that the owner gets more than initially paid. Is this an arbitrage (explain)? Hint: The values of l, and 19 are in the set {f}, {}. The values CA(0) and d are integers. 1+r 3.[8 points] Consider a 2-period CRR model with d= 0.9, r = 5%, u = 1.4 and S(0) = $100. The stock pays a $23 dividend at time 2. Consider the American call option with strike $100. (a) (4pts) Draw the payoff tree and calculate the pricing tree. At what node is the call executed before maturity? (b) (2pts) At the node from a), the option holder wants to wait and ask to change the American call into a European call with the same strike price. Using B(0) = $60, what would be the replicating strategy (80, 81) for the European call? (c) (2pts) How much refund would the owner get from changing the American call into a Euro- pean call? Check that the owner gets more than initially paid. Is this an arbitrage (explain)? Hint: The values of l, and 19 are in the set {f}, {}. The values CA(0) and d are integers. 1+r