Par Curve

The par curve is a hypotenetical yield curve for coupon-paying Treasury securities that assumes all securities are priced at par. It represents the yields to maturity on coupon-paying government bonds, priced at par, over a range of maturities. In practice, recently issued (“on the run”) bonds are typically used to create the par curve because new issues are typically priced at or close to par.

The par curve is important for valuation in that it can be used to construct a zero-coupon yield curve. The process makes use of the fact that a coupon-paying bond can be viewed as a portfolio of zero-coupon bonds. The zero-coupon rates are determined by using the par yields and solving for the zero-coupon rates one by one, in order from earliest to latest maturities, via a process of forward substitution known as bootstrapping (a statistical method for estimating a sample distribution based on the properties of an approximating distribution).

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