Consider a non-dividend paying share with a current price of 730 pence and constant volatility (standard deviation) of 20%. Assume that the annual risk-free rate is constant at 4%.

a) Use the Black-Scholes-Merton formula, together with the put-call parity, to calculate fair theoretical prices for a European call option and a European put option on the above share assuming that these options have the same exercise price of 730 pence and time to maturity of three months. (10 marks)

b) If the put option mentioned in part a) is actually selling in the derivatives market for 7 pence less than its fair price calculated in part a), but the call option is selling for the same price as that calculated in part a), describe in detail a riskless arbitrage strategy, involving both options, that takes advantage of this mispricing. Assume that the Black-Scholes-Merton equation, together with the put-call parity, is the correct model for pricing options. (30 marks)

c) Briefly describe the terms: implied volatility and option smiles. (Maximum 500 words.) (10 marks)

d) An investor would like to hedge a portfolio containing 100 of the shares mentioned in this question using European call options. How many call options does this investor have to buy or sell, and what is the total cost of this hedging strategy? Assume that fractions are allowed and indicate whether this investor has to buy the options or sell them. (10 marks)

e) How the investor, mentioned in part d), would hedge the portfolio of 1000 shares by using European put options instead? Indicate how many puts this investor has to buy or sell assuming fractions are allowed. (10 marks)

f) Compare and contrast the costs involved in the hedging strategies of parts d) and e), and discuss the issues involved in deciding on one strategy than the other. (Maximum 500 words.) (30 marks)