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

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

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

$c={\frac {1-P_{n}}{\sum _{k=1}^{n}P_{k}}}$

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.

See also

Nominal_yield