A yield curve is typically constructed on the basis of observed yields and maturities. There are different types of yield curves.

The most common type is the upward-sloping yield curve. The longer maturity issues have higher yields than the shorter maturity issues.

A spot rate is the yield on a zero-coupon bond. A series of spot rates (spot curve) can be used to discount the cash flows of a bond.

Default-free spot rates can be derived from the Treasury par yield curve by a method called bootstrapping. The basic principle of bootstrapping is that the value of a Treasury coupon security should be equal to the value of the package of zero-coupon Treasury securities that duplicate the coupon bond's cash flows.

Example

Determine the spot rate for the fourth period cash flow. The coupon rate is 4.11%, paid semi-annually.

The coupon for each period should be discounted at the corresponding spot rate.

100 = 2.055/(1+0.03/2)¹ + 2.055/(1+0.033/2)² + 2.055/(1+0.035053/2)³ + 102.055/(1+i/2)⁴ = 2.0246 + 1.9888 + 1.9506 + 102.055/(1+i/2)⁴

i = 2.0669% and the annualized spot rate is 4.1339%.

A par curve is a sequence of yields-to-maturity in which each bond is priced at par value. A par curve is obtained from a spot curve. All bonds used to derive the par curve are assumed to have the same credit risk, periodicity, currency, liquidity, tax status, and annual yields.