a. An agricultural firm has today taken a short position in 2000 commodity futures contracts at a price of $5.15. The contract size is for one unit of the underlying. The initial margin for this total position is $4,000 and the maintenance margin is $3,500. If, over the next five days, the closing futures price is $5.32, $5.29, $5.41, $5.37 and $5.35, tabulate and explain the balances in the firm’s margin account, including any margin calls. (10 marks)

b. A different agricultural firm wishes to hedge its sale of 50,000 units of a particular commodity six months from now. The current spot price of the commodity is $2,120 per unit and the continuously compounded interest rate is 2%. A futures contract with 8 months to maturity exists on this commodity. Each future has a contract size equal to one unit of the underlying asset. Assuming no storage costs or convenience yields, work out the price at which the firm enters into the futures contract today. If, six months later, the spot price of the commodity is $1,97 per unit, work out the revenue that the firm makes from the sale and the profit and loss on the hedge. Thus, what is the effective price that the firm is receiving per unit for the sale of the commodity? (10 marks)

c. Consider a short futures position on a particular stock (assuming that the stock pays no dividends) with a delivery price of K . Show how can one obtain the same payoff profile using call and put options written on the same stock. If the value of the futures position is currently zero (i.e. K is the no-arbitrage price of the future), what must be true about the prices of the options which you have used to generate the same payoff profile as the future. [HINT: put-call parity will be helpful here.] (10 marks)

d. A company wishes to hedge the price at which it will have to purchase heating oil in 2 months from now. It does not have access to a heating oil futures contract, but does have access to a 3 month jet fuel futures contract. The price changes of jet fuel and heating oil are relatively strongly correlated. Explain how the firm would construct a hedge and the risk to which it is exposed. (5 marks)