You are given the following information:
• The 1-year interest rate is 4.5% (with continuous compounding).
• The 2-year swap rate is 5.11% (with simple compounding).
• A 3-year, 7% coupon bond is priced at $104.30.
• A 4-year, 3% coupon bond is priced at $90.80.
Assume that all swaps and bonds have annual payment frequency. Bond prices are given as $ and ¢ per $100 par (not in “32nds” as customary in US bond markets).
(a) What are the spot rates (with continuous compounding) for 2, 3, and 4 years’ maturity? What are the implied discount factors?
(b) What are the implied forward rates (continuous compounding) for “1-into- 2”, “2-into-3”, and “3-into-4” years? What do these forward rates tell us about market participants’ expectations about future spot rates?
Consider a 4-year swap, in which one party will pay fixed annual interest at a rate of 6%, whilst receiving floating interest (also annually), both on a principal of $1 million.
(c) Given the rates you have calculated in parts a) and b) above, what (to the nearest $1) is the “fair” value of the swap (to the payer of fixed) (Hint: don’t forget to convert the forward rates from part b) into simple compounding!)
(d) For the swap considered in part c), what is the “swap rate” Confirm your result by re-valuing the swap, using the swap rate for the “fixed leg”. Why is the swap rate higher / lower than that of the 2-year swap?