a. i. Question 3 (answer all parts of the question) Suppose S&P 100 index is currently valued at 810 points on NYSE. The standard deviation of the index is 25% and the dividend yield is 2%, both per year with continuous compounding. European type options on S&P100 trade at CBOE. Each index option contract is for a multiple of $100. LIBOR is 5.00% per year with continuous compounding. Required (show all step-by-step calculations for each part): Calculate the cost of one European type put option contract with a strike value of 800 and maturity in six months using two-step binomial model. ii. Calculate the cost of an equivalent European type call option contract using put-call parity [30 + 15 = 45 marks] b. A fund manager will be buying a new portfolio of stocks worth $1,000,000 in six months that will track S&P 100 index. She is concerned that the markets may get bullish over this period. Use the information and your answers from Part(a) above to answer the following questions. Required (show all step-by-step calculations for each part): i. Which option and what position should she use to insure that the purchase cost of buying the portfolio does not go above $1,000,000 in six month time? ii. How many contracts should she use? iii. What would be the cost of this insurance? [13 + 10 + 7 = 30 marks] Discuss as to why a fund manager might wish to hedge an already well diversified portfolio of stocks? (maximum word count: 200) [25 marks] Total [45 + 30 + 25 = 100 marks]