The 6-month, 12-month, 18-month, and 24-month zero rates are 4%, 4.5%, 4.75%, and 5%, with semi-annual compounding.
(a) What are the rates with continuous compounding?
(b) What is the forward rate for the 6-month period beginning in 18 months?
(c) What is the value of an FRA that promises to pay 6% (compounded semi-annually) on a principal of $1 million for the 6-month period starting in 18 months?
Portfolio A consists of a 1-year zero-coupon bond with a face value of $2,000 and a 10-year zero-coupon bond with a face value of $6,000. Portfolio B consists of a 5.95-year zero-coupon bond with a face value of $5,000. The current yield on all bonds is 10% per annum.
(a) Show that both portfolios have the same duration.
(b) Show that the percentage changes in the values of the two portfolios for a 0.1% per annum increase in yields are the same.
(c) What are the percentage changes in the values of the two portfolios for a 5% per annum increase in yields?
The future price for the June 2005 CBOT bond futures contract is 118-23.
(a) Calculate the conversion factor for a bond maturing on January 1, 2021, paying a coupon of 10%.
(b) Calculate the conversion factor for a bond maturing on October 1, 2026, paying a coupon of 7%.
(c) Suppose that the quoted prices of the bonds in (a) and (b) are 169.00 and 136.00, respectively. Which bond is cheaper to deliver?
(d) Assuming that the cheapest-to-deliver bond is actually delivered, what is the cash price received for the bond?
Suppose that the term structure of interest rates is flat in the United States and Australia. The USD interest rate is 7% per annum and the AUD rate is 9% per annum. The current value of the AUD is 0.62 USD. Under the terms of a swap agreement, a financial institution pays 8% per annum in AUD and receives 4% per annum in USD. The principals in the two currencies are $12 million USD and 20 million AUD. Payments are exchanged every year, with one exchange having just taken place. The swap will last 2 more years. What is the value of the swap to the financial institution? Assume all interest rates are continuously compounded.
Solution to 4 textbook problem from 'Option, Futures and Other Derivatives, by John C. Hull' dealing with Continuous Compounding, Portfolio Duration, CBOT bond futures contract, Swap.