(a.)Carefully explain how an airline could eliminate the uncertainty of oil price movements using oil futures contracts. It is important that you include relevant details in your answer and that your answer is well structured and clear to someone who is not an expert in finance.

(b.)Draw the payoff profile of being long a put option on the day of expiry and before expiry. Clearly mark in the diagram, time value and intrinsic value if the put option is in-the money or out-of-the money.

(c.)A stock market index is S0 = 95 and the put premium for an option on the index with 1 year to expiry and a strike price of 100 costs 9.29. Short term interest rates with 1 year to maturity are 2% (simple rate).

You work for a retail bank and are asked to structure a guarantee bond using call options written on the stock market index. The guarantee bond has the following features. It guarantees to repay a customer's investment of 100 under any circumstances, but if the stock market increases it passes on the higher value. An administration fee applies which will not be repaid.

(i.) To avoid an arbitrage profit what would the call premium have to be?

(ii.) Explain how you would structure such a guarantee bond using calls.

(iii.) What would your administration fees have to be so that you could structure such a bond and break even?

(iv.) Suppose in one year's time the stock index (S1) is either 85 or 120. What would a customer receive and assuming the retail bank charges an administration fee which allows you to break even what would the return for the investor be?