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).^[1] 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^[2]

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

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

References

1. G. Questa: Fixed income analysis for the global financial market Chapter 7 Section 4;
2. Martellini, Priaulet, Priaulet: Fixed-income securities, Wiley Finance, 2003