B25: On the 31* December, a company's stock was trading at $100. Each forward contract on the company's stock is for 1,000 stocks. The quoted forward price on each contract is $103,000 for 31 October delivery. It is expected the company will pay a dividend of $2 on the 31" March. The table below shows the risk-free rates over the year. 4 months or less 4.00% More than 4 to 8 months 4.50% More than 8 to 12 months 5.00% Demonstrate clearly all the steps that must be taken to make arbitrage profit. (Show the payoffs of each step and the exact amount of arbitrage profit made from each forward contract) (Show your workings to 4 decimal places) [10m) B26 The 9-month interest rates in China and USA are 3% and 1% compounded continuously respectively. The current spot rate for USD is 6.5 RMB/USD and the 9-month forward rate is 6.451235 RMB/USD. If each forward contract is for 1,000 USD, show in details, the amounts and transactions needed to gain arbitrage profit for each forward contract. How much arbitrage profit can be made for each forward contract (Show your workings and answers to at least 4 decimal places) [10m] B27 Three call options on the same asset with the same maturity are available in the market with exercise prices: X1 = $100, X2 = $110, and X3 = $120 respectively. The three call options are priced at $2, $3 and $7. (You have to determine which of the three call options cost $2, $3 and $7 respectively) (a) Show how a butterfly spread option trading strategy can be executed using the above call options. (b) What market conditions would an investor using a butterfly spread trading strategy be expecting? (c) Sketch the payoff and profit diagram for the butterfly spread. (d) Calculate the maximum payoff and maximum profit. [10m)