BE332-6-AU/S SECTION B There are TWO questions in Section B. Candidates must answer BOTH questions. Always show your work fully. QUESTION THREE a) At time 1 0 Mr. Anderson sets up a riskless portfolio by taking a position in an option and in the underlying asset. Explain what Mr. Anderson needs to do at time t=1 to keep his portfolio risk neutral and why. (5 marks) b) A stock price is currently $100 and at the end of four months it will be Sy. A derivative written on this stock pays off exp S, /|in four months. Given that u = 1.15, d = 0.87, and that the risk-free interest rate is 10% p.a. (continuously compounded), answer the following questions using a one-period binomial model (show all the details of your calculations and display the results with four decimal places): i) Calculate the value of A (5 marks) ii) Calculate the current value of the derivative. (5 marks) c) JustHedge Corporation has the following portfolio of options, all written on the same stock which currently sells for $1,025 per share, has a volatility of 25% p.a. and pays no dividends - recall that I contract = 100 shares: Time to Expiration Number of Option type Position Strike (years) Contracts Call Long 1,000 0.5 50 Put Long 1,200 0.25 100BE332-6-ALlNG i} Using the table below and the fact that delta is given by o (I{Sa/K) + (rp + .:3;2}1") _N( aT determine the delta of the entire position assuming a continuously compounded risk- free rate of 10%0 p.a. (show all the detmls of your calculations and display the results with four decimal places). (5 marks) i1} How can you make this portfolio delta-neutral