A stock price is currently at $40. The annualized standard deviation of the stock returns is 13.48%. The risk-free interest rate is 6%.

a) Build a two-step binomial tree describing the behaviour of the stock price over the next 6 months. (4 marks)

b) Calculate the value of a European put option with a strike price of $45 and time to maturity of 6 months using a two-step binomial model. (4 marks)

c) Calculate the value of an American put option with a strike price of $45 and time to maturity of 6 months using a two-step binomial model. (4 marks)