QUESTION THREE

1. At time t=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)

2. A stock price is currently $100 and at the end of four months it will be ST . A derivative written on this stock pays off expST1/3 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):
   1. Calculate the value of

(5 marks)

2. Calculate the current value of the derivative.

(5 marks)

3. 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 1 contract = 100 shares:

Option type	Position	Strike	Time to Expiration (years)	Number of Contracts
Call	Long	1,000	0.5	50
Put	Long	1,200	0.25	100

1. Using the table below and the fact that delta is given by

=Nln(S0/K)+(rf+2/2)TT

determine the delta of the entire position assuming a continuously compounded risk-free rate of 10% p.a. (show all the details of your calculations and display the results with four decimal places).

(5 marks)

2. How can you make this portfolio delta-neutral?

(5 marks)