5. [2] (a) Explain the differences between a forward contract and an option. [2] (b) An investor has taken a short position in a forward contract. If Sr is the price of the underlying stock at maturity and K is the strike, what is the payoff for the investor? Does the investor expect the underlying stock price to increase or decrease? Explain your answer. (c) (i) An investor has just taken a short position in a 6-month forward contract on coupon-bearing bond that will mature 6 months from today is expected to pay a coupon $30 in 3 months. The bond price is $600, and the risk- free rate of interest is 4% per annum with continuous compounding for all maturities. Determine the strike, the forward price and the initial value of the forward contract. [3] (ii) If the forward price for that contract is $550, what arbitrage opportunities does this create? How much will you gain with that strategy? (iii) Four months later, the price of the bond is $540 and the risk-free rate of interest is 3% per annum. What are the strike, the forward price and the value of the short position in the forward contract? (d) Consider a 1-year forward contract on an asset that is expected to provide income equal to 3% of the asset price quarterly compounded. The risk-free rate of interest (with continuous compounding) is 5% per annum. The asset price is $25. Determine the delivery price of the forward contract if it was negotiated today (e) You are a jewellery maker and you enter into a 1-year futures contracts on gold. The spot price of gold is $1000 per ounce. The storage costs are $80 per ounce per year with the payment being made at the end of the year. Assuming that interest rates are 3% per annum for all maturities, compute a bound for the future price and the convenience yield in the case Fo = $1050. [3]