This question is based on Models for Financial Economics!

Future prices of a stock are modelled with a 3-period binomial tree, each period being 4 months. You are given the following information:

(i) The tree is constructed based on the Cox-Ross-Rubinstein binomial model. (ii) The current stock price is S0 = 40.

(iii) The continuously compounded annual risk free interest rate is 5%.

(iv) The stock pays continuous dividends at an annual rate of 2%.

(v) = 0.25.

a) Determine the price of a 1-year 45-strike European put option on this stock.

b) Calculate the number of shares and the amount of money in the replicating portfolio

at time 0 for the 1-year 45-strike European put option.

c) Determine the price of a a 1-year 45-strike American put option on this stock.