Problem 2: Binomial Trees [5 marks]

A stock price is currently $40. Over each of the next two three-month periods it is expected to go up by 10% or down by 10%. The risk-free interest rate is 7% 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 $42. [1 mark]

b. Use a two-step binomial tree to calculate the value of a six-month American put option with a strike price of $42. [1 mark]

c. Use a two-step binomial tree to calculate the value of a six-month European call option with a strike price of $42. [1 mark]

d. Show whether the put-call-parity holds for the European put and the European call. Also calculate the deltas of the European put and the European call at the different nodes of the binomial tree. Hint: You need to calculate three deltas for the call and three deltas for the put. [2 marks]