Problem Set 2 With Answers
FIN532M: Financial Derivatives
Problem Set 2
DUE DATE: Feb. 12, 2015
1. How can you differentiate the forward price from the value of a forward contract?
(2 points)
2. Explain why an FRA can be viewed as an exchange of a floating rate of interest for a fixed rate of interest payments and how you can use FRA in mitigating risks.
(4 points)
3. The standard deviation of monthly changes in the spot price of live cattle is 1.2 cents per pound. The standard deviation of monthly changes in the futures price of live cattle for the closest contract is 1.4.
The correlation between the futures price and the spot price changes is 0.7. It is now Feb 5 and a beef producer is committed to purchase 200,000 pounds of live cattle on April 10. The producer wants to use the May live-cattle futures contracts to hedge its risk where each contract is for the delivery of 40,000 pounds of live cattle. Answer the following:
a. Indicate the optimal hedge ratio.
(2 points)
b. Indicate if long or short and the optimal number of May contracts to be used.
(2 points)
4. An index is 1,200. The three-month risk-free rate is 3% per annum and the dividend yield over the next three months is 1.2% per annum. The six-month risk-free rate is 3.5% per annum and the dividend yield over the next six months is 1% per annum. All interest rates and dividend yields are continuously compounded. Estimate the futures price of the index for six-month contract.
(3 points)
5. Suppose the zero interest rates with continuous compounding are as follows. Calculate the 1-year forward interest rate for the 5th year (or the 1-year forward rate between the periods year 4 to year 5).
(3 points)
Maturity (years)
1
2
3
4
5
Rate (% per annum
2.0
3.0
3.7
4.2
4.5
6. You just entered an FRA and agreed to pay 6% per annum compounded annually at the end of third year on $1 million for the next two years. If the 5-year zero rate is 5% continuously compounded and the
3-year forward 2-year LIBOR rate is 5.6% continuously compounded.
Problem Set 2
DUE DATE: Feb. 12, 2015
1. How can you differentiate the forward price from the value of a forward contract?
(2 points)
2. Explain why an FRA can be viewed as an exchange of a floating rate of interest for a fixed rate of interest payments and how you can use FRA in mitigating risks.
(4 points)
3. The standard deviation of monthly changes in the spot price of live cattle is 1.2 cents per pound. The standard deviation of monthly changes in the futures price of live cattle for the closest contract is 1.4.
The correlation between the futures price and the spot price changes is 0.7. It is now Feb 5 and a beef producer is committed to purchase 200,000 pounds of live cattle on April 10. The producer wants to use the May live-cattle futures contracts to hedge its risk where each contract is for the delivery of 40,000 pounds of live cattle. Answer the following:
a. Indicate the optimal hedge ratio.
(2 points)
b. Indicate if long or short and the optimal number of May contracts to be used.
(2 points)
4. An index is 1,200. The three-month risk-free rate is 3% per annum and the dividend yield over the next three months is 1.2% per annum. The six-month risk-free rate is 3.5% per annum and the dividend yield over the next six months is 1% per annum. All interest rates and dividend yields are continuously compounded. Estimate the futures price of the index for six-month contract.
(3 points)
5. Suppose the zero interest rates with continuous compounding are as follows. Calculate the 1-year forward interest rate for the 5th year (or the 1-year forward rate between the periods year 4 to year 5).
(3 points)
Maturity (years)
1
2
3
4
5
Rate (% per annum
2.0
3.0
3.7
4.2
4.5
6. You just entered an FRA and agreed to pay 6% per annum compounded annually at the end of third year on $1 million for the next two years. If the 5-year zero rate is 5% continuously compounded and the
3-year forward 2-year LIBOR rate is 5.6% continuously compounded.