1. Today (time 0) the stock price of company Z is So 50. In 6 months (time t = 0.5) it changes with probability of 60% to S : = 65 and with probability 40% to S = 40, From time t 0.5 to time t 1 the stock price may increase by 20% with a probability of 80% or decrease by 30% with a probability of 20%. The risk free interest rate is constant and equal to 5% (e..). The yield curve is flat. (a) Draw a tree. (b) Use replicating portfolios to calculate the price of a European at-the-money put option with 1 year left to maturity (c) What is the price of an American at-the-money put option with 1 year left to maturity