Risk Management and Financial Institutions, + Web Site, 3rd Edition

APPENDIX B

Zero Rates, Forward Rates, and Zero-Coupon Yield Curves

The n-year zero-coupon interest rate is the rate of interest earned on an investment that starts today and lasts for n years. All the interest and principal is realized at the end of n years. There are no intermediate payments. The n-year zero-coupon interest rate is sometimes also referred to as the n-year spot interest rate, the n-year zero rate, or just the n-year zero. The zero rate as a function of maturity is referred to as the zero curve. Suppose a five-year zero rate with continuous compounding is quoted as 5% per annum. (See Appendix A for a discussion of compounding frequencies.) This means that $100, if invested for five years, grows to

A forward rate is the future zero rate implied by today’s zero rates. Consider the zero rates shown in Table B.1. The forward rate for the period between six months and one year is 6.6%. This is because 5% for the first six months combined with 6.6% for the next six months gives an average of 5.8% for the two years. Similarly, the forward rate for the period between 12 months and 18 months is 7.6%, because this rate when combined with 5.8% for the first 12 months gives an average of 6.4% for the 18 months. In general, the forward rate F for the period between times T1 and T2 is

(B.1)

where R1 is the zero rate for maturity of T1 and R2 is the zero rate for maturity T