1. Use "e" (continuously compounded) to calculate

2. Typed answer would be better. Thanks!!

1. Today (time t = 0) the stock price of company Z is So = 50. In 6 months (time t = 0.5) it changes (under the true probability measure P) with probability of 60% to Sm= 65 and with probability 40% to so = 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% (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? 1. Today (time t = 0) the stock price of company Z is So = 50. In 6 months (time t = 0.5) it changes (under the true probability measure P) with probability of 60% to Sm= 65 and with probability 40% to so = 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% (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