Problem 3: Binomial Trees (8 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 8% per annum with continuous compounding.

1. Use a two-step binomial tree to calculate the value of a six-month European put option with a strike price of $43.
2. Use a two-step binomial tree to calculate the value of a six-month American put option with a strike price of $43.
3. Use a two-step binomial tree to calculate the value of a six-month European call option with a strike price of $43.
4. Show whether the put-call-parity holds for the European put and the European call. 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.

Problem 4: Binomial Trees (5 marks)

A stock price is currently $30. During each two-month period for the next four months it is expected to increase by 8% or reduce by 10%. The risk-free interest rate is 5%. Use a two-step tree to calculate the value of a derivative that pays off where is the stock price in four months?