Problem 3: Binomial Trees (5 marks) 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. (:1. Show Whether the put-call-parity holds for the European put and the European call. e. 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 $40. During each two-month period for the next four months it is expected to increase by 10% or decrease by 8%. The risk-free interest rate is 5%. Use a two-step tree to calculate the value of a derivative that pays off (man[(ST-35),0])2 where Sr is the stock price in four months. a. Use no-arbitrage arguments (you need to show how to set up the riskless portfolios at the different nodes of the binomial tree). b. Use risk-neutral valuation. c. Verify whether both approaches lead to the same result. d. If the derivative is of American style, should it be exercised early? (continues on next page)