Question 5: 20 marks

1. Calculate the price of a three-month European call option on a non-dividend-paying stock using the Black-Scholes formula with a strike price of $50 when the current stock price is $50, the risk-free interest rate is 10% per annum, and the volatility is 30% per annum (i.e., s =0.3). (15 marks)
2. Mutual funds can effectively charge sales fees in one of three ways: front-end load fees, 12b-1 (i.e., annual) fees, or deferred (i.e., back-end) load fees. Assume that the ABC Fund offers its investors the choice of the following sales fee arrangements: (i) a 3% front-end load or (ii) a 2% back-end load, paid at the liquidation of the investors position. Also assume that ABC Fund averages NAV growth of 12% per year. If you start with $100,000 in investment capital, calculate what an investment in ABC would be worth in three years under each of the proposed sales fee schemes. Which scheme would you choose? Why? (5 marks)