1. (a) Let the present price of shares in XYZ be 150p/ share. Suppose that after one time period, the shares will be either 125p or 2007 and that you can purchase at time t =0 the option to buy shares of XYZ at time t = 1 at a price of 180p at a unit cost of c/option. Let the nominal interest rate r = 6% per time period. i. Use arbitrage to determine the value of c. r (8 marks) ii. Hence, or otherwise, find the unit cost (p/option) of a put option with a strike price of 180p (2 marks) (b) A corn farmer will harvest 20,000 bushels of corn in 3 months. Using the proceeds from the sale of the corn, the farmer plans to repay a loan of 140,000 at the same time. The price of corn today is 7 per bushel. The farmer receives some news that the price of corn might change considerably within the next 3 months, and, as a result, is very nervous about being unable to make the loan repayments. Which of the following alternatives would you recommend to the farmer? i. Buy European put options for 20,000 bushels with a strike price of 2 per bushel. ii. Sell futures contracts for 20,000 bushels with a futures price of 7 per bushel and delivery in 3 months. iii. Buy futures contracts for 20,000 bushels with a futures price of 7 per bushel and delivery in 3 months Explain your answer by describing the farmer's profit in the different scenarios. (4 marks) (e) It is known that in 9 months' time a certain share will be worth either 250p or 350p with probabilities 1/6 and 5/6, respectively. If the annual interest rate is 3%, find an upper bound for the current price of the share. (4 marks) 1. (a) Let the present price of shares in XYZ be 150p/ share. Suppose that after one time period, the shares will be either 125p or 2007 and that you can purchase at time t =0 the option to buy shares of XYZ at time t = 1 at a price of 180p at a unit cost of c/option. Let the nominal interest rate r = 6% per time period. i. Use arbitrage to determine the value of c. r (8 marks) ii. Hence, or otherwise, find the unit cost (p/option) of a put option with a strike price of 180p (2 marks) (b) A corn farmer will harvest 20,000 bushels of corn in 3 months. Using the proceeds from the sale of the corn, the farmer plans to repay a loan of 140,000 at the same time. The price of corn today is 7 per bushel. The farmer receives some news that the price of corn might change considerably within the next 3 months, and, as a result, is very nervous about being unable to make the loan repayments. Which of the following alternatives would you recommend to the farmer? i. Buy European put options for 20,000 bushels with a strike price of 2 per bushel. ii. Sell futures contracts for 20,000 bushels with a futures price of 7 per bushel and delivery in 3 months. iii. Buy futures contracts for 20,000 bushels with a futures price of 7 per bushel and delivery in 3 months Explain your answer by describing the farmer's profit in the different scenarios. (4 marks) (e) It is known that in 9 months' time a certain share will be worth either 250p or 350p with probabilities 1/6 and 5/6, respectively. If the annual interest rate is 3%, find an upper bound for the current price of the share. (4 marks)
