C1
5.3. Suppose that you enter into a 6-month forward contract on a non-dividend-paying stock when the stock price is $30 and the risk-free interest rate (with continuous compounding) is 12% per annum. What is the forward price?
Solution:
= = 31.86
5.9. A 1-year long forward contract on a non-dividend-paying 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%. What are the forward price and the value of the forward contract?
Solution:
a) = 44.21
b) = 47.31 = 45 - = 2.946
5.15. The spot price of silver is $15 per ounce. The storage costs are $0.24 per ounce per year payable quarterly in advance. Assuming that interest rates are 10% per annum for all maturities, calculate the futures price of silver for delivery in 9 months.
First we need to calculate the present value of the storage cost that has to be consider as part of the . In this sence the storage cost implies 0.06 per 3 month 0.06, so the PV of the cost of storage for 9 month is:
Now we continue calculating the price of the future including the cost of storage:
5.26. The spot price of oil is $80 per barrel and the cost of storing a barrel of oil for one year is $3, payable at the end of the year. The risk-free interest rate is 5% per annum continuously compounded. What is an upper bound for the one-year futures price of oil?
First of all we need to value to present the cost of storing
2.854
So the upper bond for the one year future price is
5.27. A stock is expected to pay a dividend of $1 per share in 2 months and in 5 months. The stock price is $50, and the risk-free rate of interest is 8% per annum with continuous compounding for all maturities. An investor has just taken a short position in a 6-month forward contract on the stock.
(a) What are the
Solution:
= = 31.86
5.9. A 1-year long forward contract on a non-dividend-paying 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%. What are the forward price and the value of the forward contract?
Solution:
a) = 44.21
b) = 47.31 = 45 - = 2.946
5.15. The spot price of silver is $15 per ounce. The storage costs are $0.24 per ounce per year payable quarterly in advance. Assuming that interest rates are 10% per annum for all maturities, calculate the futures price of silver for delivery in 9 months.
First we need to calculate the present value of the storage cost that has to be consider as part of the . In this sence the storage cost implies 0.06 per 3 month 0.06, so the PV of the cost of storage for 9 month is:
Now we continue calculating the price of the future including the cost of storage:
5.26. The spot price of oil is $80 per barrel and the cost of storing a barrel of oil for one year is $3, payable at the end of the year. The risk-free interest rate is 5% per annum continuously compounded. What is an upper bound for the one-year futures price of oil?
First of all we need to value to present the cost of storing
2.854
So the upper bond for the one year future price is
5.27. A stock is expected to pay a dividend of $1 per share in 2 months and in 5 months. The stock price is $50, and the risk-free rate of interest is 8% per annum with continuous compounding for all maturities. An investor has just taken a short position in a 6-month forward contract on the stock.
(a) What are the