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

$\frac{100 c}{1 + R(0,1)} + \frac{100 c}{(1 + R(0,2))^2} + \cdots + \frac{100 + 100c}{(1+R(0,n))^n } = 100.$

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

$c=\frac{1-P_n}{\sum_{k=1}^nP_k}$

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

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