Question 1 a. A stock price is currently $30. It is known that at the end of two months it will be either $33 or $27. The risk-free interest rate is 10% per annum with continuous compounding. What is the value of a two-month European put option with a strike price of $31? b. What is meant by the delta of a stock option? A stock price is currently $100. Over each of the next two three-month periods it is expected to go up by 8% or down by 7%. The risk-free interest rate is 5% per annum with continuous compounding. What is the value of a six-month European call option with a strike price of $952 I (3+2+5= 10 marks) C. Question 2 a. What are the assumptions behind the Black-Scholes-Merton model? b. Compute the price of a European call option on a non-dividend paying stock with the strike price is $70 when the stock price is $73, the risk-free interest rate is 10% pa, the volatility is 40% pa, and the time to maturity is 6 months? c. Without using the Black-Scholes model, compute the price of a 6 month European put on the same stock in b) with strike price of $70. I (3+4+3 = 10 marks) Question 3 a. What a company should do to hedge foreign currency that will be received or paid? Explain your answer. b. What are advantages of futures options over spot options? c. What does vega measure? What can you tell from vega value? Can the vega of a derivatives portfolio be changed by taking a position in the underlying asset? Explain your answer. (3+3+4 = 10 marks) Question 4 A non-dividend - paying stock with a current price of $52, the strike price is $50, the risk free interest rate is 12% pa, the volatility is 30% pa, and the time to maturity is 3 months? a) Calculate the price of a call option on this stock b) What is the price of a put option price on this stock? c) Is the put-call parity of these options hold? (4 + 4 + 2 = 10 marks)