1. A stock is expected to pay a dividend of $3 in eight months. A one-year long forward contract on the stock is entered into when the stock price is $40 and the risk-free rate of interest is 10% per annum with continuous compounding. a. What are the forward price and the initial value of the forward contract? b. Six months later, the price of the stock is $45 and the risk-free interest rate is still 10%. (i) What are the forward price, and change in forward price from six months ago. (ii) Briefly describe in words what the value of the initial forward contract is. (iii) Show the appropriate equation for calculating the value of the initial forward contract and then calculate the value of the initial forward contract if forward price is $49 now.
2. The current price of palm oil is $12 per gallon. The storage costs are $0.36 per gallon per annum payable monthly in advance. Assume that the interest rates are 12% per annum with continuous compounding for all maturities. Show the appropriate equations and then calculate per gallon (a) storage cost, (b) accrued interest, (c) total carrying cost, and (d) the future price of palm oil for delivery in three months.
3. A $100 million interest rate swap has a remaining life of 10 months. Under the terms of the swap, the six-month LIBOR is exchanged semi-annually for 12% per annum. The six-month LIBOR rate in swaps of all maturities is currently 10% per annum with continuous compounding. The six-month LIBOR rate was 9.6% per annum two months ago. What is the current value of the swap to the party paying floating? What is its value to the party paying fixed?