= = = Today (time t 0) the price of a stock is So 100. In 6 months (time t 0.5) the stock price may change (under the true probability measure P) with probability of 60% to su 120 or with probability 40% to see = 70. 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% per year (c.c.). 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) Use risk neutral probabilities to price a European at-the-money put option with 1 year left to maturity. (d) What is the price of an American at-the-money put option with 1 year left to maturity? = = = Today (time t 0) the price of a stock is So 100. In 6 months (time t 0.5) the stock price may change (under the true probability measure P) with probability of 60% to su 120 or with probability 40% to see = 70. 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% per year (c.c.). 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) Use risk neutral probabilities to price a European at-the-money put option with 1 year left to maturity. (d) What is the price of an American at-the-money put option with 1 year left to maturity