A stock price is currently $30. Over each of the next two three-month periods it is expected to go up by 8% or down by 10%. The risk-free interest rate is 5% per annum with continuous compounding. a. Use a two-step binomial tree to calculate the value of a six-month European put option with a strike price of $32. b. Use a two-step binomial tree to calculate the value of a six-month American put option with a strike price of $32. c. Use a two-step binomial tree to calculate the value of a six-month European call option with a strike price of $32. d. Calculate the deltas of the European put and the European call at the different nodes of the binomial three. Hint: You need to calculate three deltas for the call and three deltas for the put.