Question 4 A. A stock price is currently $40. Over each of the next two 3-month periods it is expected to go up by 10% or down by 10% The risk-free interest rate is 12%% per annum with continuous compounding. What is the value of a 6-month European put option with a strike price of $429 (5 Marks) B. From Question 4A, what is the value of a 6-month American put option with a strike price of $429 (5 Marks) C. A stock price is currently $30. During each 2-month period for the next 4 months it will 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 [max (30-St, Of. where Sr is the stock price in 4 months. If the derivative is American-style, should it be exercised carly? (5 Marks) D. Consider a European call option on a non-dividend-paying stock where the stock price is $40, the strike price is $40, the risk-free rate is 4% per annum, the volatility is 30% per annum, and the time to maturity is 6 months. (5 Marks) i Calculate u, d, and p for a two-step tree. ii. Value the option using a two-step tree. E. Repeat Question 4D for an American put option on a futures contract. The strike price and the futures price are $50, the risk-free rate is 10%, the time to maturity is 6 months, and the volatility is 40% per annum. (5 Marks) EXAMINER: Saint Kuttu, PhD Page 4 of 4