Maturity Structure of Interest Rates
Suppose that the yield-to-maturity is higher on one bond compared to another bond. There are several possible reasons for the difference, including credit risk, different currencies, liquidity, tax differences, and the periodicity assumption used in the yield calculation.
This factor explaining the differences in yields is called the maturity structure of interest rates or term structure of interest rates.
Term structure is best analysed using bonds that have all the same properties other than time-to-maturity; that is, the bonds should be denominated in the same currency and have the same credit risk, liquidity, tax status, and periodicity assumption and they should have the same coupon rate so that they each have the same degree of coupon reinvestment risk.
This ideal dataset would be yields-to-maturity on a series of default-risk-free zero-coupon bonds, known as spot rates, for a full range of maturities. Developed market sovereign bonds are typically used for this purpose, because they represent the lowest default risk among issuers in a given market. Collectively, this dataset is the government bond spot curve, sometimes called the zero or “strip” curve (because the coupon payments are “stripped” off the bonds).
Bond Pricing Using Spot Rates
A general formula for calculating a bond price given the sequence of spot rates. Note that for pricing a bond with a different risk profile than the spot curve (such as credit risk, as for corporate bonds, for example), a spread would have to be added to the spot rates.
where
- Z1 is the spot rate, or zero-coupon yield or zero rate, for period 1
- Z2 is the spot rate, or zero-coupon yield or zero rate, for period 2
- ZN is the spot rate, or zero-coupon yield or zero rate, for period N
