Par yield

Par yield (or par rate) denotes in finance, the coupon rate for which the price of a bond is equal to its nominal value (or par value). It is used in the design of fixed interest securities and in constructing interest rate swaps.

The par yield c for a n-year maturity fixed bond satisfies the following equation

100 c 1 + R ( 0 , 1 ) + 100 c ( 1 + R ( 0 , 2 ) ) 2 + ⋯ + 100 + 100 c ( 1 + R ( 0 , n ) ) n = 100.

This can be more succinctly expressed with the prices of zero coupon bonds:

c = 1 − P n ∑ k = 1 n P k

Here R ( 0 , n ) denotes the yield (on annual interest rate basis) of an n -year zero-coupon bond, and P n denotes the price of an n -year ZCB.