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]

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

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

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

Here $R(0,n)$ 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